IMAGE  EVALUATION 
TEST  TARGET  (MT-S) 


1.0 


I.I 


18 


1.25  III  1.4   111.6 


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7 


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Photographic 

Sciences 

Corporation 


23  WEST  MAIN  STREET 

WEBSTER,  N.Y.  14580 

(716)  872-4503 


^^ 

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:\ 


iV 


CIHM/ICMH 

Microfiche 

Series. 


CIHJVi/ICIVIH 
Collection  de 
microfiches. 


Canadian  Institute  for  Historical  MicroreprodJictions  /  Institut  Canadian  de  microreproductions  historiques 


Tttchnical  and  Bibliographic  Notaa/Notas  tachniquas  at  bibiiographiquaa 


The  Instituta  has  anamptad  to  obtain  tha  bast 
original  copy  availabia  for  filming.  Featuras  of  this 
copy  which  may  ba  bibliographically  uniqua, 
which  may  altar  any  of  tha  imagas  in  tha 
raproduction,  or  which  may  significantly  changa 
tha  uaual  mathod  of  filming,  ara  chackad  balow. 


□    Coloured  covers/ 
Couverture  de  couleur 


I      I    Covers  damaged/ 


n 


D 


D 


n 


Couverture  endommagAa 


Covers  restored  and/or  laminated/ 
Couverture  restaurie  et/ou  pelliculAe 


I      I    Cover  title  missing/ 


Le  titre  de  couverture  manque 


I      I    Coloured  maps/ 


Cartes  gtegraphiquas  en  couleur 


Coloured  ink  (i.e.  other  than  blue  or  black)/ 
Encra  de  couleur  (i.e.  autre  que  bleue  ou  noirel 


r~l    Coloured  platea  and/or  illustrations/ 


Planches  et/ou  illustrations  •»  couleur 


Bound  with  other  material/ 
Reliift  avac  d'autras  documents 


Tight  binding  may  cause  shadows  or  distortion 
along  interior  margin/ 

La  re  liure  serrde  peut  causer  de  I'ombre  ou  de  la 
distorsion  le  long  da  la  marge  int6rieure 

Blank  leaves  added  during  restoration  may 
appear  within  the  text.  Whenever  posaibla,  these 
have  been  omitted  from  filming/ 
II  se  peut  que  certainea  pages  blanches  ajoutiaa 
lors  d'une  restauration  apparaissent  dana  le  texte. 
mala,  lorsqua  cela  Atait  possible,  ces  pages  n'ont 
paa  iti  filmtes. 


L'Institut  a  microfilm*  le  meilleur  exemplaire 
qu'll  lui  a  it*  possible  de  se  procurer.  Las  details 
de  cet  exemplaire  qui  sont  peut-Atre  uniques  du 
point  de  vue  bibliographiqua,  qui  peuvant  modifier 
una  image  reproduite,  ou  qui  peuvent  exigar  una 
modification  dans  ia  mtthoda  normale  de  fiimaga 
sont  indiquto  ci-dessous. 


□   Coloured  pages/ 
Pagaa  de  couleur 


D 
0 
0 
0 


D 


Pagaa  damaged/ 
Pagea  endommagiea 

Pages  restored  and/or  laminated/ 
Pages  restauries  et/ou  pelliculAes 

Pages  discoloured,  stained  or  foxed/ 
Pages  dicolories,  tacheties  ou  piquias 

Pages  detached/ 
Pages  dAtach6as 

Showthrough/ 
Transparence 


The  c 
to  thi 

I 

i 

Theii 
possi 
of  th( 
filmir 


Origii 
begin 
theic 
sion, 
other 
first  I 
sion. 
or  ilk 


I      I    Quality  of  print  varies/ 


Quality  inigalo  de  I'impression 

Includes  supplementary  material/ 
Comprand  du  material  supplimentaire 

Only  edition  available/ 
Seule  Mition  disponible 


Theli 
shall 
TINU 
whici 

Maps 

differ 

entire 

begin 

right 

requii 

meth 


Pagea  wholly  or  partiitMy  obscured  by  errata 
slips,  tissues,  etc.,  have  been  ref limed  to 
ensure  the  best  possible  image/ 
Lea  pages  totalement  ou  partiallement 
obscurcies  par  un  feuillet  d'errata,  una  pelure, 
etc.,  ont  M  filmies  d  nouveau  de  fa^on  i 
obtenir  la  meilleure  image  possible. 


Fyj    Additional  comments:/ 


Commentaires  supplAmentaires: 


Paget  53  &  54  are  miuing. 


This  item  is  filmed  at  the  reduction  ratio  checked  below/ 

Ce  document  est  film*  au  taux  de  rMuction  indiqui  ci-dessous. 

10X  14X  18X  Z2X 


26X 


30X 


y 


12X 


16X 


20X 


24X 


28X 


] 


32X 


The  copy  filmed  here  has  been  reproduced  thanks 
to  the  generosity  of: 

Harold  Camptoll  Vaughan  Memorial  Library 
Acadia  Univanity 

The  images  appearing  here  are  the  best  quality 
possible  considering  the  condition  and  legibility 
of  the  original  copy  and  in  Iteeping  with  the 
filming  contract  specifications. 


L'exemplaire  fllmA  fut  reproduit  grAce  k  la 
gAntrositA  de: 

Harold  Campbell  Vaughan  Memorial  Library 
Acadia  University 

Les  images  suh^antes  ont:  At4  reproduites  avec  le 
plus  grand  soin,  compte  tenu  de  la  condition  et 
de  la  nettet*  de  rexemplaire  filmA,  et  en 
conformity  avec  les  conditions  du  contrat  de 
filmage. 


Original  copies  in  printed  paper  covers  are  filmed 
beginning  with  the  front  cover  and  ending  on 
the  last  page  with  a  printed  or  illustrated  impres- 
sion, or  the  bacic  cover  when  appropriate.  All 
other  original  copies  are  filmed  beginning  on  the 
first  page  with  a  printed  or  illustrated  impres- 
sion, and  ending  on  the  last  page  with  a  printed 
or  illustrated  impression. 


Les  exemplaires  originaux  dont  la  couverture  en 
papier  est  imprimte  sont  filmte  en  commen^ant 
par  le  premier  plat  et  en  terminant  soit  par  la 
derniire  page  qui  comporte  une  empreinte 
d'impression  ou  d'illustration,  soit  par  le  second 
plat,  salon  le  cas.  Tous  les  autres  exemplaires 
originaux  sont  filmto  en  commenpant  par  la 
premiere  page  qui  comporte  une  empreinte 
d'impression  ou  d'illustration  et  en  terminant  par 
la  derniAre  page  qui  comporte  une  telle 
empreinte. 


The  last  recorded  frame  on  each  microfiche 
shall  contain  the  symbol  — »>  (meaning  "CON- 
TINUED"), or  the  symbol  V  (meaning  "END"), 
whichever  applies. 


Un  des  symboles  suivants  apparattra  sur  la 
dernlAre  image  de  cheque  microfiche,  selon  le 
cas:  le  symbole  — ►  signifie  "A  SUIVRE",  le 
symbols  V  signifie  "FIN". 


Maps,  plates,  charts,  etc.,  may  be  filmed  at 
different  reduction  ratios.  Those  too  large  to  be 
entirely  included  in  one  exposure  are  filmed 
beginning  in  the  upper  left  hand  corner,  left  to 
right  and  top  to  bottom,  as  many  fr<imes  as 
required.  The  following  diagrams  illustrate  the 
method: 


Les  cartes,  planches,  tableaux,  etc.,  peuvent  Atre 
filmte  A  des  taux  de  reduction  diff6ients. 
Lorsque  le  document  est  trop  grand  pour  Atre 
reproduit  en  un  seul  clichA,  11  est  filmA  A  partir 
de  I'Gngle  supArieur  gauche,  de  gauche  A  droite, 
et  de  haut  en  bas,  en  prenant  le  nombre 
d'imagee  nAcessaire.  Les  diagrammes  suivants 
illustrent  la  mAthode. 


1 

2 

3 

1 

2 

3 

4 

5 

6 

\ 


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A. 


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A 


THE 


TUTOE^S  ASSISTA%T; 

BKINO  A 

COMPENDIUM  OF  ARITHMETIC, 

AND 

COMPLETE  QUESTION-BOOK; 

CONTAINING, 
V 

I.  Arithmetic  in  whole  pumbers ;  being  a  brief  explanation  of  all  its  Rules,  in  a  new 
and  more  concise  method  than  any  hitherto  published ;  with  an  Application  to  each 
Rule,  consisting  of  a  great  variety  of  questions  in  real  Business,  with  their  answers 
annexed. 

II.  Vulgar  Fractions,  which  ars  treated  with  a  great  deal  of  plainness  and  perspicuity 

III.  Decimals,  with  the  extraction  of  the  Square,  Cube,  and  Biquadrate  Roots,  after  a 
very  plain  and  familiar  manner ;  to  which  are  added,  Rules  for  the  easy  calculation  of 
Interest,  Annuities,  and  Pensions',  in  arrears,  &o.,  either  by  Simple  or  Compound  Interest. 

IV.  Duodecimals,  or  Multiplication  of  Feet  and  Inches,  with  Examples  applied  to 
measuring  and  working  by  Multiplication,  Practice,  and  Decimals. 

y.  A  Oa^Sfl^jOn  of  Questions,  promiscuously  arranged,  for  the  exercise  of  t^ .'  c  cholar 
in  the  foreg^l^ules. 

TO  WHICH  ARE  ADDED, 

A  new  and  very  short  method  of  extracting  the  Cube  Root,  and  a  General  Table  for 
readily  calculating  the  Interest  of  any  sum  of  money,  at  any  rate  per  cent. ;  Rents, 
Salaries,  &c. 

The  whole  being  adapted  either  as  a  Question-Book  for  the  use  of  Schools,  or  as  a 
Remembrancer  and  Instructor  to  such  as  have  some  knowledge  of  Accounts. 

This  Work  having  been  perused  by  several  eminent  Mathematicians  and  Accountants, 
is  recommended  as  the  best  Compendium  hitherto  published,  for  the  use  of  Schools,  or 
for  private  persons. 

BY    FRANCIS    WALKINGAME, 

WEITINO-MASTKR  AND  ACCOUNTANT. 


TO  WHICH  IS  ADDED, 

A  COMPENDIUM  OF  BOOK-KEEPING, 

BY   ISAAC   FISHER. 


NEW-YORKt 
PUBLISHED    BY 


D.  &  J.  SADLIER  &  CO.,  164  WiLLIAM-STRiSiSi. 
BOSTON  :-128  FEDERAL  STREET. 
AND  179  NOTRE- DAME  STREET,  MONTREAL:  C.  E.* 

1851. 


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/^■/t'^'l 


PREFACE. 


The  public,  no  doubt,  will  be  surprised  to  find  there  is  another 
attempt  made  to  publish  a  book  of  Arithmetic,  when  there  are 
Ruch  numbers  already  extant  on  the  same  subject,  an*  several 
of  them  that  have  so  lately  made  their  appearance  in  the  world ; 
but  I  flatter  myself,  that  the  following  reasons  which  induced 
roe  to  compile  it,  the  method,  and  the  conciseness  of  the  rules, 
which  are  laid  down  in  so  plain  and  famiUar  a  manner,  will 
have  some  weight  towards  its  having  a  favourable  reception. 

Having  some  time  ago  drawn  up  a  set  of  rules  and  proper  ques- 
tions, with  their  answers  annexed,  for  the  use  of  my  own  school, 
and  divided  them  into  several  books,  as  well  for  more  ease  to 
myself,  as  the  readier  improvement  of  my  scholars,  I  found  them 
by  experience,   of  infinite  use;   for  when  a  master  takes  upon 
him  that  laborious,  (though  unnecessary,)  method  of  writing  out 
the  rules  and  questions  in  the  children's  books,  he  must  either  be 
toiling  and  slaving  himself  after  the   fatigue  of  the  school  is 
over,  to  get  ready  the  books  for  the  next  day,  or  else  must  lose 
that  time  which  would  be  much  better  spent  in  instructing  and 
opening  the  minds  of  his  pupils.     There  was,  however,  still  an 
inconvenience  ^hich  hindered  them  from  giving  me  the   satis- 
faction I  at  first  expected ;  i.  e.  where  there  are  several  boys  in  a 
class,  some  one  or  other  must  wait  till  the  boy  who  firet  has  the 
book,  finishes  the  writing  out  of  those  rules  or  questions  he  wants, 
which  detains  the  others  from  making  that  progress  they  other- 
wise might,  had  they  a  proper  book  of  rules  and  examples  for 
each ;  to  remedy  which,  I  was  prompted  to  compile  one  in  order 
to  have  it  printed,  that  might  not  only  be  of  uso  to  my  own 
school,  but  to  such  others  as  would  have  their  scholars  make  a 
uuick  progress.     It  will  also  be  of  great  use  to  such  gentlemen  9^ 
^  A3     t>^^(^^  ^ 


- 


IV 


w 


PREFACE. 


have  acquired  some  knowledge  of  numbers  at  school  to  make  them 
the  more  perfect;  hkewise  to  such  as  have  completed  themselves 
therein,  it  will  prove,  after  an  impartial  perusal,  on  account  of  ite 
great  variety  and  brevity,  a  most  agreeable  and  entertaming  exer- 
L-book.  I  shall  not  presume  to  say  any  thing  more  m  favour  of 
this  work,  but  beg  leave  to  refer  the  unprejudiced  reader  to  the 
remark  of  a  certain  author,*  concerning  compositions  of  this  nature. 
His  words  are  as  follows : — 

«  And  now,  after  all,  it  is  possible  that  some  who  like  best  to 
tread  the  old  beaten  path,  and  to  sweat  at  their  business,  when 
they  may  do  it  with  pleasure,  may  start  an  objection,  agamst^e 
use  of  this  well-intended  Assistant,  because  the  course  of  anth- 
metic  is  always  the  same ;  and  therefore  say,  that  some  boys  lazily 
inclined,  when  they  see  another  at  work  upon  the  ^ame  ques  on 
will  be  apt  to  make  his  operation  pass  for  their  own     But  ih^e 
Uttle  forgeries  are  soon  detected  by  the  diligence  of  the  tutor 
thereforeras  different  questions  to  different  boys  do  not  in  the  least 
promote  their  improvement,  so  neither  do  the  questions  hinder  it 
tfeither  is  it  in  the  power  of  any  master  (in  the  course  of  his  busi- 
ness) how  full  of  spirits  soever  he  be,   to  frame  new   questions 
at  pleasure  in  any  rule :  but  the  same  question  will  frequently  oc- 
cur in  the  same  rule,  notwithstanding  his  greatest  care  and  skill  to 

^'irma7also  be  further  objected,  that  to  teach  by  a  printed 
book  is  an  argument  of  ignorance  and  incapacity ;  which  is  iio  less 
triflin-  than  the  former.  He,  indeed,  (if  any  such  there  be,)  who 
is  afraid  his  scholars  will  improve  too  fast,  will,  undoubtedly,  decry 
tJiis  method :  but  that  master's  igorance  can  never  be  brought  in 
question,  who  can  begin  and  end  it  readily;  and,  most  certainly, 
that  scholar's  non-improvement  can  be  as  little  questioned,  who 
makes  a  much  greater  progress  by  this,  than  by  the  common 
method. 

To  enter  into  a  long  detail  of  every  rule,  would  tire  the  reader, 
and  swell  the  preface  to  an  unusual  length;  I  shall,  therefore,  only 
give  a  general  idea  of  the  method  of  proceeding,  and  leave  the 
rest  to  speak  for  itself;  which  I  bopc  the  kind  reader  will  find  to 
answer  the  title,  and  the  recommendation  given  it.     As  to  the 


Dilworth. 


'-    «"« 


i^iiii    11'  m 


PBEFACB.  ' 

rules,  they  follow  in  the  same  manner  as  the  table  of  coni^nts 
specifies,  and  in  much  the  same  order  as  they  are  generally  taught 
in  schools.     I  have  gone  through  the  four  fundamental  rules  in  In- 
tegers first,  before  those  of  the  several  denominations;   in  order 
that  thev  being  well  understood,  the  latter  will  be  performed  with 
much  more  ease  and  dispatch,  according  to  the  rules  shown,  then 
by  the  customary  method  of  dotting.     In  multiphcation  I  have 
shown  both  the  beauty  and  use  of  that  excellent  rule,  in  resolvmg 
most  questions  that  occur  in  merchandising;   and  have  prefixed 
l)efore  Reduction,  several  Bills  of  Parcels,  -which  are  applicable  to 
real  business.  In  working  Interest  by  Decimals,  I  have  added  tables 
to  the  rules,  for  the  readier  calculating  of  Annuities,  &c.  and  have 
not  only  shown  the  use,  but  the  method  of  making  them  :  as  like- 
wise an  Interest  Table,  calculated  for  the  easier  finding  of  the  Inte- 
rest of  any  sum  of  money  at  any  rate  per  cent,  by  Multiplication 
and  Addition  only ;  it  is  also  useful  in  calculating  Rates,  Incomes, 
and  Servants'  Wages,  for  any  number  of  months,  weeks,  or  days;, 
and  I  may  venture  to  say,  I  have  gone  through  the  whole  with  so 
much  plainness  and  pei-spicuity,  that  there  is  none  better  extant. 

I  have  nothing  further  to  add,  but  a  return  of  my  sincere  thanks 
to  all  those  gentlemen,  schoolmasters,  and  others,  whose  kind  ap- 
probation and  encouragement  have  now  established  the  use  of  this 
book  in  almost  every  school  of  eminence  throughout  the  kmgdom : 
but  I  think  my  gratitude  more  especially  due  to  those  who  have 
favoured  me  with  their  remarks ;  though  I  must  still  beg  of  every 
candid  and  judicious  reader,  that  if  he  should,  by  chance,  find  a 
transposition  of  a  letter,  or  a  false  figiu-e,  to  excuse  it;  for,  not- 
withstanding  there  has  been  great  care  taken  in  correcting,  yet  errors 
of  the  press  will  inevitably  creep  in ;  and  some  may  also  have  shp- 
ped  my  observation;  in  either  of  which  cases  the  admomtion  of  a 
good-natured  reader  will  be  very  acceptable  to  his  much  obliged, 
and  most  obedient  humble  servant,  „r  a  t  Tr^xrn  a  mt? 


_ 


ARITHMETICAL    TABLES 


NUMERATION. 

Units             1  I  X.  of  Thousands 12,345 

Tens 12     C.  of  Thousands 123,450 

Hundreds'.'.'. 123  I  Millions 1,234,507 

Thousands 1,234     X.  of  Millions 12,345,673 


Note.— This  Table  may  be  applied  to  Division  by  reversing  it;  as  the 
\''i4  in  4  are  2,  and  23  in  6  are  3,  &c. 


fl^l»»« 


ARITHMKTICAL    TABLES. 


Vll 


20d 

24 

30 

36 

40 

48 

50 

60 

70 

T2 


PENCE. 

are  Is.  8d 
..2  0 
6 
0 
4 
0 
2 
0 
10 
0 


2 
3 
3 
4 

4 
5 
5 

6 


TABLES  OF  MONEY. 
2()3,  are  £1 


80d,  are 

81  .. 

90  .. 

U6  .. 

100  .. 

108  .. 

110  .. 

120  . . 

130  .. 

1 140  .. 


Ga. 

7 

7 

8 

8 

9 

9 
10 
10 
11 


8d. 
0 
6 
0 
4 
0 
2 
0 
10 
8' 


30 
40 
50 
00 
70 
80 
90 
100 
110 


1 

2 

2 

3 

3 

4 

4 

5 

5 


Os. 
10 

0 
10 

0 
10 

0 
10 

0 
10 


hHILLINCS. 

1208.  are  £6 


130 
140 
150 
160 
170 
ISO 
190 
200 
210 


6 
7 
7 
8 
8 
9 
9 
10 
10 


Os. 
10 

0 
10 

0 
10 

0 
10 

0 
10 


OF  A  POUND. 


lOs, 
6 
5 
4 
3 
2 
2 
1 
1 
0 
0 


Od 

8.. 

0.. 

0.. 

4.. 


is  1 
..1 
..1 
..1 
.1 


6. . .  .1 


0. 
8. 
8. 
8. 
6. 


.'.1 
..1 
..1 

I  •  •  -L 

...1 


half 

third 

fourth 

fifth 

sixth 

eighth 

tenth 

twelfth 

twentieth 

thirtieth 

fortieth 


PRACTICE  TABLES. 

OF  A  SHII^LING. 

6d.      is      1  half 

4 1  third 

3 1  fourth 

2 1  sixth 

ll 1  eighth 

1 1  twelfth 

OF  A  TON. 

10      cwt.      1  half 

5 1  fourth 

4 1  fifth 

2i 1  eighth 

2 1  tenth 


qrs. 
2 
1. 
0. 
0. 


or 


OF  A  CWT. 

lb. 

56  is  1 
..28....1 
.  .16. . .  .1 
.  .14. . .  .1 


half 
fourth 
seventh 
eighth 


OF  A  QUARTER. 

14lbs 1  half 

7 1  fourth 

4 1  seventh| 

3i 1  eighth 


CUSTOMARY  WEIGHT  OF  GOODS. 

Firkin  of  Butter  is 56  Ibs.iA  Stone  of  Glass. -5  lb.s.| 

*  -  "•  A  Stone  of  Iron  oj  bhot 14 

A  Barrel  of  Anchovies ..30 

A  Barrel  of  Pot  Ashes 200 

A  Seam  of  Glass,  24  Stone, 
or 120 


A  Firkin  of  Soap 64 

A  Barrel  of  Soap 256 

A  Barrel  of  Butter 224 


A  Barrel  of  Candles 
A  Faggot  of  Steel . . 


120 
120 


TABLES 

TBOY  WKIGHT. 

24  gr..inake  1  dwt. 

20dvvt 1  ounce 

12  oz 1  poullfd 

apothecaries' 
20  gr.  make  1  scruple, 

3  bcr 1  dram. 

8  dr 1  ounce 

12  oz 1  pound 


OF 


WEIGHTS  AND 

WOOL  WEIGHT. 

7  lbs.  make  1  clove 
2  cloves....!  stone 

2  stone 1  tod 

6i  tods 1  wey 

2  weys. .....  1  sack 

12  sacks 1  last 


MEASURES. 

land  measure. 

9  feet  make  1  yard 

30  yards  .>  . .  1  pole 

40  poles 1  rood 

4  roods  i . .  .1  acre 


I 


AVOIRDUPOIS. 

16  dr.  make  1  oz. 

16  oz 1  lb. 

14  1b 1  stone 

28  lb 1  quarter 

4  qrs 1  cwt. 

20  cwt 1  ton, 


CLOTH  MEASURE. 


2i  inch  make 
4    nails 

quar.; 

quar 

nnav. . . . . . 

quar 


3 
4 
5 
6 


nail 
quar. 
Fl.  ell 
yard 
En.  ell 
Fr.  ell 


LONG  MEASURE. 

3    bar.  corn  1  inch 
inches  . .  1  foot 

feet 1  yard 

feef 1  fathom 


(SOLID  MEASURE. 

172S  in.  make  1  sol.  ft. 
27  feet I  ynrd 


12 

3 

6 

5^  yards  . 
40    poles. . 

8    funn  . . . 

3  miles  . 
69^  miles. 


t  i- 

pole 

•  1 

furlon; 

mile 

•  k. 

lenjrne 

•   X 

degree 

m 


vtu 


AKITIIMHTK  AL    TAKLES. 


OLD  STANDARD. 


Gals. 

0 

0 
0 

8 

n 

35 
53 

70 
10() 


Q. 

0 
0 
3 
3 
2 
1 
0 
3 
0 


P. 

Gills. 

0 

3.i)3 

I 

3.8C 

1 

3.46 

0 

3.17 

1 

2.34 

1 

0.69 

0 

3,03 

0 

1.3S 

1 

2.06 

0 

1 

12 

21 

50 

75 

100 

151 

302 


1 

0 

0 

2 

1 

2 

3 

0 

1 


0 

1 

0 
0 

1 

0 
0 

1 
1 


1.00 

2.41 

0.10 

3.28 

1.22 

3.S3 

2.44 

3.06 

3.33 


B.  P.  G. 

0    0    0 
0    0    1 

0  1    0 

1  0    0 

2  0    0 


Q. 
1 
0 
0 

1 

2 


P. 
0 
0 
0 
0 
0 


Gills. 
0.25 
1.01 
2.02 
0.07 
0.14 


4 

0 

1 

0 

0 

0.28 

8 

1 

0 

0 

0 

0.56 

33 

0 

0 

0 

0 

2.24 

82 

2 

0 

0 

1 

1.63 

ALE  AND  BEER. 


NKW  STANDARD. 


gills  make 

pints 

([uarts. ... 
Ijallons. . . 
firkins. .. 


1 

I 

,  1 

.1 

.1 


pint 

quart 

gal. 

tir. 

kild. 

bar. 


kilderkins.  1 
li  ban-el 1  hhd 

2  barrels 1  pun. 

3  barrels 1  butt 


WINE  MEASURE. 


2  pints. . .  1  quart 
4  quarts..,!  gallon 
10  gallons..  1  anker 
IS  gallons..!  runlet 
42  gallons..!  tierce 
63  gallons..!  hogshead 
84  gallons..!  puncheon 
2  hhds...l  pipe 
2  pipes...!  tun 


DRY  MEASURE. 


3 

37 

0 
0 

0 
1 

3 

0 

0 
0 

0.21 
2.52 

2  pints  make  1  quart 

4  quarts 1  gallon 

2  gallons ....  1  peck 

4  pecks 1  bushel 

2  bushels....  1  strike 
4  bushels.  ...1  sack 

8  bushels 1  quarter 

4  quarters...  1  chald. 
10  quarters...  1  last 


COAL  MEASURE. 


31    0 

77    2 


"W 


3  bushels..!  sack  2    3 

36  bushels..!   chaldron]  34    3 


0.52 
2.34 


n 


CONTENTS. 


PART  L— ARITHMETIC  IN  WHOLE  NUMBERS 


Page. 

Introduction ^^ 

Numeration J3 

Integers,  Addition 15 

. Subtraction 16 

Multiplication 16 

D^ision 19 

Tables .•  •  Jl 

Addition  of  several  denominationsSS 

Subtraction 34 

Multiplication 37 

Division 42 

Bills  of  Parcels 44 

Reduction •  47 

Single  Rufe  of  Three  Direct. . .  53 

~~ -Inverse..  56 

Double  Rule  of  Thre«, -  58 

Practice 23 

Tare  and  Tret 6/ 

Simi)le  Interest i^ 

Commission 

Purchasing  of  Stocks 


71 
71 


PART  II.— VULGAR  FRACTIONS 


iOG 


Reduction 

Addition Jl;^ 

Subtraction H- 

Multiplication 113 


Page. 

Brokerage "'^ 

Compound  Interest "j^ 

Rebate  or  Discount 75 

Equation  of  Payments 70 

Barter H 

Profit  and  Loss ^y 

Fellowship °y 

vsithoutTime »0 

_ —with  Time 82 

Alligation  Medial 83 

Alternate o*^ 

Position,  or  Rule  of  False 88 

Double 90 

Exchange •  • • ; ;  •  • 

Comparison  of  Weights  and  Mea- 
sures   • 

Conjoined  Proportion 

Progression,  Ariir.hmetical 97 

. Geometrical 100 

Permutation 104 


95 
96 


Division. 


The  Rule  of  Three  Direct....  114 

Inverse....  115 

The  Double  Rule  of  Three. . .   HJ 


.-  X 


■^ 


CONTENTS. 


t^A 


PART  III.— DECIMALS. 


11^ 

119 
120 


Page. 

Numeration '■'■' 

Addition ]\° 

Subtraction 

Multiplication 

Contracted  Multiplication.. 

Division ]^\ 

Contracted l'*'* 

Reduction ;  •  •  •  •  •.•  •  •  1^3 

Decimal  Tables  of  CoinjWeights, 

and  Measures 126 

The  Rule  of  Three -129 

Extraction  of  the  Square  Root. 

. Vulgar  Fractions 

-Mixed  Numbers. 

Extract  of  the  Cube  Root. . . . 

Vulgar  Fractions . . . 

Mixed  Numbers. . . . 

^ ^Biquadrate  Root. . . . 


130 
131 
132 
134 
136 
136 
138 


Page. 

A  general  Rule  for  extracting  the 

Roots  of  all  powers 138 

Simple  Interest 140 

. . for  days 141 

Annuities  and  Pensions,  Hcc.  in 

Arrears 1^3 

Present  worth  of  Annuities. . .  147 
Annuities,  &c.  in  Reversion.. .  150 

Rebate  or  Discount l'^>2 

Equation  of  Payments l-)* 

Compound  Interest l'^--> 

Annuities,  &c.  in  Arrears IT)? 

Present  worth  of  Annuities.. .   160 
Annuities,  &c.  in  Reversion. . .   102 
Purchasing  Freehold  or  Real  Es- 
tates  i'5J 

in  Reversion .......  l*^)) 

Rebate  or  Discount 160 


PART  IV.r-DUODECIMALS. 


Multiplication  of  Feet  &  Inches,  169 
Measuring  by  the  Foot  Square,  171 
Measuring  by  the  Yai-d  Square,  171 
Measuring  by  the  Square  of  100 


F^et. 


173 


Measuring  by  the  Rod 1^3 

Multiplying  several  Fijipres  by 
several,  and  the  operation  in 
one  line  only 1'''^ 


PART  V.-QUESTIONS. 


A  Collection  of  Questions,  set 
down  promiscuously  for  the 
greater  trial  of  the  foregoing 
Rules 1'^^ 

A  COMPENDIUM  OF  BOOK-KEEPING 


A  general  Table  for  calculating 
Interests,  Rents,  Incomes  and 
Servants'  Wages 181 


184 


63 


^ 


u  e. 


EXPLANATION    OF   THE   CHARACTBB8. 


EXPLANATION 

= Equal. 

— ^Minus,  or  Less. 

4- Plus,  or  More. 

X  Multiplied  by. 

^Divided  by. 

235Y 

63 
;  :  So  is. 

7^2 +5  =  10. 

9__24-5=2. 

^/ 

-y 

« 


OF  THE  CHARACTERS  MADE  USE  OF  IN 
THIS  COiMPENDIUM. 

The   Sign  of  Equality ;   as,  4  qrs.  =  1  cwt 
signifies  thaj.  4  qrs.  are  equal  to  1  cwt. 

The  Sign  of  Subtraction;  as,  8—2=6,  that 
is,  8  lessened  by  2  is  eqpl  to  6. 

Tbe  Sign  of  Additional  1»s,  4+4=8,  that  is, 
4  added  to  4  more,  is  equal  to  8. 

The  Sign  of  Multiplication;   as,  4X6  =2i, 
that  is,  4  multiplied  by  6  is  equal  to  24. 

The  Sign  of  Division ;  as,  8+2=4,  that  is, 
8  divided  by  2  is  equal  to  4. 

Numbers  placed  like  a  fra<5tion  do  likewise 
denote  Division ;  the  upper  number  bemg  the 
dividend,  and  the  l^er  %e  divisor. 

The  Sign  of  Proportion ;  as,  2  :  4  : :  8  :  16, 
that  is,  as  2  is  to  4,  so  is  8  to  16. 

Shows  tlg^the  difference  between  2  and  7 
added  tJf,  is  equal  to  10. 

Signifil^f  the  sum  of  2  and  5  taken  fi-om 
9,  is  equ4  to  2. 

Prefixed  *  any  number,  signifies  the  Square 
Boot  of  that  number  is  required. 

Signifies  the  Cube,  or  Third  Power. 

T^ +^0   fhA  Tiinnadrate.  or  Fourth  Power, 


1 


i      I 


id  est,  that  is. 


y 


/ 


/' 


TT] 


I 


ARITH^ 

bers,  and 

all  its  ope 

Notat: 

riPLIOATIi 


i# 


Teadieth 
and  to  rei 


» 


\ 


THB 


TUTOR'S  ASSISTANT; 


BEING 


A  COMPENDIUM  OF,,ARITHMETIC. 


ARITMETI 
TH 


ERS. 


INtRdOTC^ 


Aritkmetio  is  the  Art  or  Scier^bf  computing  by  Num- 
bers, and  has  five  principal  or  fundamantal  Rules,  upon  whicU 
all  its  operations  depend,  viz : — 

Notation,   or  Numeration    Addition,   Subtraction,   Mui** 

riPLicATiON,  and  D^ision. 

^  NUMERATION        ^^^ 

Teacheth  the  diflferent  value  of  Figures^Hu^^^rent  Places, 
and  to  read  and  write  any  Sum  oi|lium| 

*THE#A'BLE. 


#^ 


n 


.«._. 


14 


NUMERATION. 


2ATI0N.  • 

following  Numbers.         ^ 


THE 


fiftl 


Write  down^ 
(»)  Twenty-thi 

H  or&enSilbirVtwo  Thousand,  Two  Hundred 
"t'f  FoAuons,  Nine  Hundred  and  Forty^ne^  Thousand, 
^7^  Tweniiiie    Millions,    One    Hundred     and     Fifty^ven 

-^iWrtv-nS^^^^M^ive  Hundred  and  ^oiir. 


Thousand,  Five  Hurilre 

Write  down  in  Wo^d^ 
n     35  O     2017' 

ri     59  Jl   0     5?01 
V    172#    n  20766 

(")  61700047         C*) 

Notatvm 

I  One. 

II  Two. 

III  Three. 

IV  Four. 
^*      V  Jbive. 

VI  Six. 

VII  Seven. 

\  vm  %ht. 


.<•> .  .^ 


ig  following  Numbers. 
7  ("^     5207054 

158  (")     2071909 

10030  (")  Jj|g4008 

(")  22lfPl90 

iters. 

IX  Nine. 

X  T^. 

XI  Eleven. 

XII  fclve. 
;Yii|  yji.irt.^.on. 

:l^en. 

XV  Fifteen. 

XVI  Sixteen. 


'■>x 


ADDITION    OF   IlfTEOERS. 


16 


% 


XVIII 

Eighteen. 

XIX 

Nineteen. 

XX 

Twenty. 

XXX 

Thirty. 

XL 

Forty. 

L 

Fifty.  • 

LX 

Sixty. 

LXX 

Seventy. 

LXXX  Eighty. 

XC 

Ninety. 

c 

Hundred 

00 

Two  Hundred 

ccc 
cccc 

D 

DC 

DCC 

JDCCC 

DCCCC 

M 

MDcccx;n. 

MDCCCXXXVil 


Three  Hundred. 
Four  Hundred. 
Five  Hundred. 
Six  Hundred. 
Seven  Hundred. 
Eight  Hundred. 
Nine  Hundred. 
One  Thousand. 
One  Thousand  Eight 
Hundred  and  Twelve. 
Thousand 'Eight 

dred  and  Thirty 

-^■ 
iven. 


INTEGERS. 
•       ADDITION 

Teacheth  to  add  two  or  more  Suras  together,  to  make  one  whole 
or  total  Sura.  j|^ 

'  Rule.  Thei^e  must  be  due  regard  lia4  in  pjglg  the  Figures 
one  under  the  other,  i.  e.  Units  underiUnit^Pns  under  Tens, 
&«. ;  then  beginning  with  the  first  row  of4tTnfCs,  add  them  up  to 
the  top;  when  done,  set  down  the  Units,  and  carry  the  Tens  to 
the  next,  and  so  on;  continuing  to  the  last  row,  under  which 
set  down  the  Total  amount.      ,  .  , 

Proof.   Begin  at  the*  top  o 
downwards,  the  same  as  yo 
the  first,  the  Sum  is  suppose 

Months. 


(•)  275 
110 
473 
354 
271 
352 


^_  Sum,  and  reckon  the  Figures 
J  them  up,  and,  il  the  same  as 
right. 


C)  1234 
7098 
3314 
6732 
2546 
6709 


W- 


£ 

(•)  75245 
37502 
91474 
32145 
47258 
21476 


Years 
(*)  271048 
325476 
107584 
625608 
754087 
279736 


^  ^  /  Ans.  U7206. 

n  x\dd  246034,  298765,  47321,  58653,  64218,  53t«,  9821,^' 
and  640  together.  ^W5.  730828. 

t2 


16 


StTBTRACTION    OP   INTEGERS. 


0  If  you  give  A.  £56,  B.  £104,  C.  £274,  D.  £391,  and  E. 

£703,  how  much  is  given  all  ?  ,      ^  ,     ,     ^,^'^,f-  }^^^' 

(*)  How  many  days  are  in  the  twelve  Calendar  Months  i 
^^  ^         -  AnB.  365. 

SUBTRACTION 

Teacheth  to  take  a  less  Number  from  a  greater,  and  shows  the 
remainder  or  difference. 

Rule  This  being  the  reverse  of  Addition,  you  must  borrow 
here  (if  it  require)  What  you  stopped  at  there,  always  remember- 
ing to  pay  it  to  the  next. 

Proof.  Add  lhe*remainder  and  the  less  Line  tog^her,  and 
if  the  same  as  the  greater,  it  is  right. 

i^\  (n  0  (*)  (')  O 

From  271       4754       42087        452705        271508        3750215 
Take  164       2725       34096        327616     '  152471        3150874 


Rem.  117 


Proof  271       -'*:, 


-# 


H 


2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 


MULTIPLICATION 

Teacheth  how  to  increase  the  gpter  of  two  Numbers  given  as 
dften  as  there  are  Units  in  the  less;  and  compendiously  performs 
the  office  of  many  additions.      ^| 

To  this  Rule  belong  three  fpncipal  Members,  viz. 

1.  The  Multiplicand,  or  Number  to  be  multiplied. 
'2.  The  Multiplier,  or  Number  by  which  you  multiply. 
8.  The  Product,  or  Number  produced  by  multiplying. 

Rule.  Begin  with  that  Figure  which  stands  in  the  Unifs  place 
of  the  Multiplier,  and  with  it  multiply  the  first  figure  in  the  Unit's 

Tens  in  mind,  till  you  have  multiplied  the  next  Figure  in  the 
Multiplicand  by  the  same  Figure  in  the  Multiplier;  to  the  pro- 
fluot  of  which  add  the  Tens  you  kept  in  mind,  setting  down  tha 
Unite,  and  proceed  as  before,  till  the  whole  line  is  nmltiplied. 


MULTIPLICATION    OP   INTEOBBS. 


19 


Proof.  By  casting  out  the  Nines;  or  «^f^\>^^,^.  ^^^'"^  .^"^- 
tiplicand  the^Multipliir,  and  the  Mult^lier  the  Multiphcaiid'  and 
it"  the  Product  of  this  operation  be  the  same  as  before,  the  work 


is  right. 


MULTIPLICATION  TABLE. 


4 


6 


■I? 

''    8 
ul2 


4 

.  6 

8 

10 

12 

6 

9 

12 

15 

18 

8 

12 

16 

20 

24 

10 

16 

20 

25 

30 

12 

W 

24 

30 

36 

14 

21 

28 

35 

42 

16 

24 

32 

40 

48 

18 

27 

36 

45 

54 

20 

30 

40 

50 

60 

22 

33 

44 

55 

66 

24 

36 

48 

60 

72 

Multiplicand 
MultipUer 


Q  25104736 
2 


•  Product  50209472 


(*)  27104107 
6 


(*)  231047 
6 


8 


9  10  11  12 


14  16 

21  24 

28  32 

35  40 

42  48 

49  56 

56  64 

63  72 

70  80 

77  88 

84  96 


18  20  22 

27  30  33 

36  40  44 

45  60  55 

54  60  66 

63  70  77 

72  80  88 

81  90  99 

90  100  110 

99  110  121 

108  120  132 


24 

36 

48 

60 

72 

84 

96 

108 

120 

132 

144 


i 
I 

A 
A 
A 
A 
A 
A 
A 

A 

A 
A 


C)  52471021   0  7925437521 


n  7092516 

7 


-A, 


(')  3725104 

8   M 


-wt 


n  4215466    (•)  2701057    {")  31040171 
9  10  11 


When  the  Multiplier  is  more  than  12,  and  less  than  20,  mulU- 
ply  by  the  Unit  Figure  in  the  Multiplier,  adding  to  tho  Produc* 
the  back  figure  to  that  you  multiphed. 

b3  y 


18 


MULTIPLICATION   OP  INTEGERS. 


(»)  5710592         (")  6107252         (")  7653210 
13  14  15 


(")  92067166 
16 


(")  6251721      -  ('«)  9215324         (")  2571341  ('')  3592104 

IV  18  19  20 


When  the  Multiplier  consists  of  several  Figures,  there  must 
be  as  many  products  as  there  are  Figures  in  the  Multiplier,  ob- 
serving to  put  the  first  figure  of  every  Product  under  that  Figure 
you  multiply  by.  Add  the  several  Products  together,  and  their 
Sum  will  be  the  total  Product. 

(")  Multiply  271041071  by  5147. 

O  Multiply  62310047  by  16G8. 

(")  Multiply  170925164  by  7419. 

n  Multiply  9500985742  by  61879. 

n  Multiply  1701495868567  by  4768756. 

When  Ciphers  are  placed  between  the  significant  Figures  in 
flie  Multiplier,  they  may  be  omitted ;  but  great  care  must  be  taken 
that  the  next  Figure  must  be  put  one  place  more  to  t£e  left  hand, 
L  e.  under  the  Figure  you  multiply  by. 

(")  Multiply  571204 
By  27009 

5140836  • 
«  3998428 

1142408 


Product      15427648836 


P')  Multiply  7561240325  by  57002. 
(")  Multiply  562710934  by  590030. 

yhen  there  are  Ciphers  at  the  end  of  the  Muitiijlicand  or  Aul- 
fijdier,  they  may  be  omitted,  by  only  multiplying  by  the  rest  of 
Ike  Figures,  and  setting  down  on  the  right  hand  of  the  total 
Product  as  many  Ciphers  as  virere  omitted. 


n  M 

Whei 
Figures 
multiply 
plied  by 


Teachei 

or,  to  d 

In  t] 

dental : 

1.  T 

2.  T 

3.  T 
is  contj 

4.  C 
finishe( 

RUL 

contaiij 
the  Fi, 
next  ii 
Diviso] 


*..ii*v.,(».^^_^^ 


blVIBION    OF   IMTE0ES8. 

(*»)  Multiply  131^500 
3400 


55180 
41385 

4690300000 

'n  Multiply  7271000  by  52600. 
(")  Multiply  V4837000  by  975000. 

When  the  Multiplier  is  a  composite  Number,  *.  e.  if  any  two 
Figures  being  multiplied  together,  will  make  that  Number,  then 
multiply  by  one  of  those  figures,  and  that  Product  bemg  multi- 
plied by  the  other  will  give  the  answer. 

(»)  Multiply  771039  by  35,  or  7  times  5. 
"^  '  *^*'  7X5=25 


5397273 
5 

26986365 


Multiply  921563  by  32.  * 

Multiply  715241  by  56. 
Multiply  7984956  by  144. 

DIVISION  % 

Teacheth  to  find  how  often  one  Number  is  contained  in  another; 
or,  to  divide  any  Number  into  what  parts  you  please. 

In  this  Rule  there  are  three  numbers  real,  and  a  fourth  acci- 
dental: viz. 

1.  The  Dividend,  or  Number  to  be  divided : 

2.  The  Divisor,  or  Number  by  which  you  divide : 

3.  The  Quotient,  or  Number  that  shows  how  often  the  Divisor 
is  contained  in  the  Dividend :  i.  i    • 

4.  Or  accidental  Number,  is  what  remains  when  the  work  is 
finished,  and  is  of  the  same  name  as  the  Dividend. 

Rule.  When  the  Divisor  is  less  than  12,  find  how  often  it  is 
contained  in  the  firat  Figure  of  the  Dividend;  set  it  down  under 
the  Figure  you  divided,  and  carry  the  Overplus  (if  any)  to  the 
next  in»the  Dividend,  as  so  many  Ter-  •  then  find  how  often  the 
Divisor  is  contained  therein,  set  it  dov...,  and  continue  the  same 


90  DIVISION    OF   INTEGERS. 

till  you  have  gone  through  the  Lino;  but  when  the  Divisor  i« 
more  than  12,  multiply  it  by  the  Quotient  Figure ;  the  Product 
subtract  from  the  Dividend,  and  to  the  Remainder  bring  down 
the  next  Figure  in  the  Dividend  and  proceed  aa  before,  till  the 
Figures  are  all  brought  down. 

Proof.  Multiply  the  Divisor  and  Quotient  together,  adding 
the  Remainder,  (if  any,)  and  the  Product  will  be  the  same  as  tlw 
Dividend. 


Dividend.  Rem. 
(*)     Divi3or.2)725l07(l 


Quotient 

362553 
2 

Proof 

725107 

7)2532701 ( 

., 

0)     3)7210472(  (»)     4)7210416( 


O    5)7203287(  (•)     6)5231037( 


O    8)2547325( 


(")     9)25047306( 


^^■|            Divisor.  Dividend.  Quotient. 
^H                 (')  29)4172377(143875 

(")  Divide 

(")  Divide 
(")  Divide 
(»)  Divide 

(")  Divide 

^B                         127 
^H                         116 

^^H                             112 

1294875 
287750 

2  rem. 

^R ' 

4172377  Proof. 

(»)  Divide 

^H                           232 

(")  Divide 

^■i                          217 
^W                         203 

^H              Rem. 

• 

7210473  by  37. 

Arts.  194877|4 
42749467  by  347. 
734097J43by  5743. 
1610478407 

by  54716, 
4973401891 

by  510834. 
51704567S74 

by  4765043. 
17453798946123741 
by  31479461, 


When  there  are  Ciphers  at  the  end  of  the  Divisor,  they  may 
be  cut  off,  and  as  many  places  from  off  the  Dividend,  but  they 
must  be  annexed  to  the  Remainder  at  last. 


1'**. 


TABLES   OF   MONfiY 


ai 


(")  271100)254732121(939 
(»)  3731000)7324731729(2017 


(»")  5721100)7253472116(1267 
(«•)  215I0001G3251041997( 

29419 


When  the  Divisor  is  a  composite  number,  i.  e.  if  any  two  Fi- 
ssures, being  multipHed  together,  will  make  that  number,  then,  by 
dividing  tlie  Dividend  by  one  of  those  Figures,  and  that  Quotient 
by  the  other,  it  will  give  the  Quotient  required.  But  as  it  some- 
times happens,  that  there  Is  a  Remainder  to  each  of  the  Quotients, 
and  neither  of  them  the  true  one,  it  may  be  found  by  this 

Rule.  Multiply  the  first  Divisor  into  the  last  Remainder,  to 
that  Product  add  the  first  Remainder,  which  will  give  the  true 
one. 

(")  •  (•»)  n  n 

Div.  3210473  by  27.      7210473  by  35.      6251043  by  42.      5761034  by  54. 
118906  11  rem.    20G013  18  rem.     148834  15  rem.      1066S5  44rem. 


Marked 
i  Farthing 
i  Halfpenny 
f  Three  Farthings 
Farthings 
4  = 


MONEY. 


.M 


4  Farthings  make  1  Penny d. 

12  Pence 1  Shilling. . .  .*. 

20  Shilhngs 1  Pound £ 


1  Penny 
48  =     12  =     1  Shilling 
960  =  240  =  20  =  1  Pound. 


SHILLINGS. 


PENCE   TABLE. 


a. 

£       s. 

d. 

s. 

d. 

d. 

s.       d. 

20 

•..  1  :  0 

20 

..  1  : 

8 

90  .. 

7  :  6 

30 

..  1  :  10 

24 

..  2  : 

0 

96  .. 

8  :  0 

40 

..  2^  :  0 

30 

..  2  : 

6 

100  .. 

8  :  4 

50 

..  2  :  ro 

36 

..  3  : 

0 

108  .. 

9  :  0 

60 

..  .  3  :  0 

40 

..  3  : 

4 

110  .. 

9  :  2 

70 

..  3  :  10 

48 

..  4  : 

0 

120  . 

10  :  0 

80 

..  4  :  0 

50 

..  4  : 

2 

130  .. 

10  :  10 

90 

..  4  :  10 

60 

..  5  : 

0 

132  . 

.  11  :  0 

100 

..  5-:  0 

70 

..  5  : 

10 

140  . 

.  11  :  8 

110 

..  5  :  10 

72 

..   6  ! 

0 

144  .. 

,  12  :  0 

120 

..6:0 

80 

..  6  : 

8 

150  .. 

12  :  6 

130 

..  6  :  10 

84 

..  7  i 

.  0  . 

160  . 

■  13  ''  K 

'* 


I 


22 


TABLES   OF   WBI0HT8. 


TROY  WEIGHT.  Marked 

2^4  Grains. ..... .make. 1  Pennyweight >  \v/t. 

20  Pennyweights 1  Ounce oz. 

12  Ounces 1  Pound lb. 

Grains 

24  =       1  Pennyweight 
480  r=     20  =     1  Ounce 
5760  =   240  =   12   =   1  Pound 

By  this  Weight  are  weighed  Gold,  Silver,  Jewels,  Electuariea 
and  all  Liquors. 

N.B.  The  Standard  for  Gold  Coin  is  22  Carats  of  fine  Gold, 
ind  2  Carats  of  Copper,  melted  together.  For  Silver,  is  11  oz. 
i  dwts.  of  fine  Silver,  and  10  dvvts.  of  Copper. 

25  lb.  is  a  quarter  of  100  lb.  1  cwt. 

20  cwt.  1  Ton  of  Gold  or  Silver. 

AVOIRDUPOIS  WEIGHT. 


16  Drams make. . .  .1  Ounce 


Marked 
)dr. 

j  oz. 

16  Ounces 1  Pound lb. 

28  Pounds 1  Quarter qr. 

4  Quarters  or  112  lb 1  Hundred  Weight cwt 

20  Hundred  Weight 1  Ton ton. 

Drams 

1  Ounce 
16  =         1  Pound 
448  ==       28  =     1  Quarter 
1792  =     112  =     4  =     1  Hundredweight 


A  Wei 

'Si 

AClov 

A  Ston 

A  To<l 

By  I 

turo ;  a 

tais  but 

Note 

gra.  Tr( 

20  Gra 

3  Sen 

8  Dra 

12  Oui 

16  = 

266  = 

7168  = 

28672  = 


673440   =   35840   =   2240 


80  =  20  ==   1  Ton. 


There  are  several   other  Denominations  in  this  Weigh,   that. 
are  used  in  some  particular  Goods,  viz. 

lb.  lb. 

A  Firkin  of  Butter 66  A  Stor-  of  Iron,  Shot  or  ) 

^    ,  .     64       Hor     nan's  wt j  ^* 

. .      SO                   Butcher's  Moat. .  8 

....  266  A  Gallon  of  Train  Oil. . . .  7^ 

Raisins   .....   112  A  Truss  of  Straw 36 

A  Puncheon  of  Prunes  ...  1120                     New  Hay  ....  60 

A  Fodder  of  Lead 19  cwt.                     Old  Hay  .....  66 

2  qrs.  .  36  Trusses  a  Load. 


Soap  . 

A  Barrel  of  Anchor. 

Soap 


-«.«. 


0 


TABLES    OP   WEIGHTS. 


as 


Cheese  and  Butter. 

A  clove  or  Half  Stone,  8  lb. 
A  Wey  in  Suffolk,  )  lb.  A  Wey  is  Essex, 

32  Cloves,  or  J  250  32  Cloves,  or 

Wool. 


)1K 
f3c 


IK 
330 


lb. 

A  Clove 1 

A  Stone 14 

ATod 28 


I  lb. 
J  181 


82 
364 
4368 


A  Wey  ia  6  Tods  and 

1  Stone,  or 
A  Sack  is  2  Weys.  or 
A  Last  is  12  Sacks,  or 

By  tliis  Weight  is  weighed  anything  of  a  coarse  or  drossy  na- 
tnr.^;  as  all  Grocery  and  Chandlery  Wares ;  Bread,  and  all  M^ 
tais  but  Silver  and  Gold. 

Note.  One  Pound  Avoirdupois  is  equal  to  14  oz.  11  dwts.  15^ 
grs.  Troy. 

APOTHECARIES'  WEIGHT. 

Marked 

20  Grains make 1     Scruple 9 

3  Scruples l     Dram ' 3 

8  Drams   i     Ounce I 

12  Ounces i     Pound lb. 

Grains 
%  20  =       1  Scruple 

60  =   3=1  Dram 
480  =  24  =  8  =  1  Ounce 
#      6760  =  288  =  96  =  12  =  1  Pound. 

Note.  The  Apothecaries  mix  their  Medicines  by  this  Rule^ 
but  buy  and  sell  their  commodities  by  Avoirdupois  Weight. 

The  Apothecaries'  Pound  and  Ounce,  and  the  Poimd  anfl 
Ounce  Troy,  are  the  same,  only  differently  divided  and  subdivi- 
ded. 


4  Nails make 1 

3  Quarters 

4  Quarters 

6  Quarters 

6  Quarters 


CLOTH  MEASURE. 

Marked 

Quarter  of  a  Yard  !■  "' 

Flemish  Ell FL  R 

Yard yd. 

English  Ell E.  E. 

French  Ell., Fr.^ 


1 
1 
1 
1 


34 


TABLES   OF   MEA8URB8. 


Inches 

2i  =    1  Nail 

9    =    4  =  1  Quarter 

36    s=  16  =  4  =  1  Yard 

27    =  12  =  3  =  1  Flemish  Ell 

'45    =  20  =  5  =  1  English  Ell 

54    =  24  =  G  =  1  French  Ell. 

LONG  MEASURE. 


3  Barley  Corns. . . .make 1  Inch. i 


Marked 

bar.  c. 
in. 
12  Inches 1  Foot feet. 

3  Feet 1  Yard yd. 

6  Feet. 1  Fathom tth. 

54  Yards 1  Rod,  Pole  or  Perch rod,  p 

40  Poles 1  Furlong fur. 

S  Furlongs 1  Mile mile. 

3  Miles 1  League lea. 

60  Miles 1  Degree deg. 

Barley  Corns 

3  =  1  Inch 

36  =        12  =        1  Foot 
lOS  =        36  =        3  =        1  Yard 
594  ^      198  =      16^=        5h=      1  Pole 
23760  =    7920  =    600  =    220  =    40  =  1  Furlona: 
190080  =  63360  =  5280  =  1700  =  320 


8  =  1  Mile. 


N.  B.   A  Degree  is  69  Miles,  4  Furlongs,  nearly,  though  com- 
monly reckoned  but  60  Miles.        ^ 

Tliis  Measure  is  used  to  measure  Distances  of  Places,  or  any 
thing  else  that  hath  length  only.    *        .  , 


All  : 
and  Oil 
law,  but 


2  Pint 

4  Qua) 

8  GalL 

9  Gall 
2  Firk 
4  Firk 
UBarr 

2  Barr( 

3  Barr( 


""•"W^ 


WINE  MEASURE. 


Marked 
)pts. 

'  ■  5  qts. 

Quarts 1  Gallon gal. 

Gallons 1  Anker  of  Brandy ^ank. 


2    Pints make 1  Quart. 


vjiaLtOnS  I 


.1  Rp-nlet ,,.,.... n 


Gallons Half  an  Hogshead k  hhd. 

Gallons 1  Tierce .tier. 

Gallons 1  Hogshead- •. hhd. 

Hogsheads 1  Pipe  or  Butt Per B. 

r^^ipes  or  4  Hogsheads .1  Tun t. 


*  By  a  late 
Dry  Measure 
Measures,  w 
"  Impnial  M 


^ 


TABLES    OF   MEASURES.  •     25 

Inches* 

28^=:      1  Pint 
57|=s      2=      1  Quart 
231  =8=      4=    1  Gallon 
9702  =  330=  108=  42=1  Tierce 
14553  =  504=  252=  63=U=1  Hogshead 
19404  =  072=  33Q=  84=2  =U=1  Puncheon 
29100  =1008=  504=120=3  ==2  =li=l  Pine 
58212  =2010=1008=252=6  =4  =3  =2  =  1  Tun 

AH  Brandies,  Spirite  Perry,  Cider,  Mead,  Vinegar,  Honey, 
and  Oil,  are  measured  by  this  measure ;  as  also  Milk,  not  by 
law,  but  cusiom  only.  ^ 

ALE  AND  BEER  MEASURE. 


2  Pints make i  Quart , 

J  Quarts 1  Gallon 

\  ^^  )°"» • 1  Firkin  of  Ale. . 

9  C^allons i  Firkin  of  Beer. 

2  Firkins j  Kilderkir 


Marked. 

5qts. 
....gal.' 
....A.  fir 
....B.  fir. 

4  Firkins,  or  2  Kilderkins,.... .1  Barrei.T."." ! ! ! *. ! .' ! .* .* ." bar 

UBarrel,  or  54  Gallons l  Hogshead  of  Beer.  ...*..'.'  .'hhd 

2  Barrels i  Puncheon 

3  Barrels,  or  2  Hogsheads 1  Butt .'.*.'.*."*.**.*,' .*  * .*  * .'C 

BEEB. 

Cubic  Inches 

354=    1  Pint 
70^=    2=    1  Quart 
282  =    8=:    4=    1  Gallon 
2538  =  72=  30=    9=  1  Firkin 
5076  =144=  72=  18=  2=1  Kilderkin 
J?iS  =^S8=144=  36=  4=2=1  Barrel 
15228  =432=210=  54=  6=3=U=l  Hoeshead 
20304  =570=288=  72=  8=^1=2  —U--1P.m?1..«« 
-        30456  =804=^132=108=12=0=3  i*=U=l  Butt 

ALE. 

Cubic  Inches 

354=    1  Pint 
70i=    2=    1  Quart 
282  =    8=    4=  1  Gallon 
2256  =  64=  32=  8=1  Firkin 

oni?  Zi?^=  04=10=2=1  Kilderkin 
oyj^ti  — ca.j=ri^o=oi;=4s=:2=i  Barrel 
13536  «384=192=48=6=3=li=^l  Hogshead, 


Dr7N?eLuts:'hav?bernr°el;l'dtr;s^^^^^^    of  the  Wi„e.  tTTITe  and  Beer,  and  the 


^ip^'l'^- 


.  iiiiwiiimi^ 


26 


TABLES    OF   MEASXTRE8. 


♦    l^„t  R  frillons  to  tlie  firkin  of  Ale, 
In  .^ndon  they  compute  bu    8  gallons  ^^^  ^^^^ 

and  32  to  the  barrel ;  but  -^^^^",^^1,  and  8^  gallons 

strong  beer  and  small,  34  gallons  w 

to  the  firkin. 

N.  B.-A  barrel  of  salmon^^^^  eels  is  42  gallons. 

A  barrel  of  herrings B        ^^^^^^^ 

A  keg  of  sturgeon -  |         ^  ^ 

A  firkin  of  soap ^  & 

DRY  MEASURE. 

Marked 
)  pts. 

make  1  Q"*"^* >^*^- 

^^'^'''- "  ...iPottle P«*- 

2Quart8 ^  Gallon. 

^p«^i\!!^ •;;:::;:::::i....ipeck. 


.gal 
.pk. 


2Gall6n8 J  Bushel ^"•., 

4  Pecks ;\|"4e '^''^ 

2  Bushels Icoom ^°°°*- 

4  Bushels ••*••; i  Quarter %\ 

2  Cooms.  or  8  Bushels J  C haldi-on . . -. ''^''^ 

4  Quarters J  Vey way. 

OQuarters \  V^I last. 

aWeys 

In  London,  36  bushels  make  a  chaldron. 

Solid  Inches 

268|=     1  Gallon 
6371=:     2=     1  Peck 
2150*=     8=     4=   1  Bushel 
43004=   16=     8=  2=   1  Stnke 
86011=   32=   16=  4=   2=  l^^^ 
,wof,oi—  64=   32=   8=  4=  2=  1  V^uarwT 
860?6'=320=160=40=20=10=  5  =  1  Wey 
m032  =640=320=80=40=20=10=2=1  Last. 

The  Bushel  in  Water  Measure  is  5  Pecks. 

»       ,  Je     21  chaldrons. 

A  score  of  coals is 3  ^hels. 

12  sacks. 


n^^lr     ^%.4>     rk/'vn  Its 


N 


!"**., 


A  chaldron  of  coals t  bushels 

Aloadofcorn i  S!k 

A  cart  of  ditto ..... .40  bushels. 

This  measure  is  applied  to  a U  dry  goods. 
The  standard  bushel  is  18^  inches  wide,  and  8  inches  deep. 


40 

4 

640 

30 
100 


i^"-*'^'  ■-•■1!|. 


TABLES   OF   MEASURES. 


87 


TIME. 


60  Seconds make....l  Minute. 

60  Minutes i  Hour... 

24  Hours i  Day.... 

7  J)«>s 1  Week.*." 

4  Weeks i  Month. 


Marked 

\" 

)  m. 
..hour. 
..day. 
. .  week. 


13  Months,  1  day,  6  hours. .  1  Julian  Year yr 


mo. 


Seconf^s 

60  =  1  Minute 

3600  =         60  =       1  Hour 

86400  =      1440  =     24  =      1 

604800  =    10080  =   168  =      1 

2419200  =  40320  =  672  =  28 

31657600=525960=8766=365  :  6= 
31556937=525948=8765=365  :  5  ; 


Day 

=  1  Week 
=  4  =  1  Month, 
w.    d.   h. 
=52:  1  :6=]  Julian  Year, 
m.     " 
48  :  57=1  Solar  Year. 


To  know  the  days  in  each  month,  observe, 

Thirty  days  hath  September, 
April,  June,  and  November, 
February  hath  twenty-eight  alone, 
And  all  the  rest  have  thirtv  and  one ; 
Except  in  Leap- Year,  and  then's  the  timo 
February's  days  are  twenty  and  nine. 

SQUARE  MEASURE. 


Foot. 


144    Inches make i 

9     Feet ^  y^^.^ 

l?oilHl 1  Squaie  of  flooring. 

'"'i^y 1  K'Hi. 

Acres'  "''  "'"  ^^^^  ^"^^ ^  ^^-''^  "^  ^''"'^ 


40 

4 

640 

30 
100 


'?^'*'^ I  Square  Mile 

^^''^^ 1  Yard  of 


Acres 


C3 


Yard  of  land. 
Hide  of  land. 


28 


ADDITION    OF   MONEY. 

Inches  ,  ^:^    * 

144=         1  Fo^t    .  ^    , 

39204=     272^=30^-      i   ^   ^  ^^^^ 
1568160  =  10890  =1210  --  4U  ^  ^^re. 

6272640=43560  =4840  -160 

4  oil  tl^inffs  that  have  length  and 
By  this  measure  -  V^^/^^^^  flooring,  thatching, 

breadth ;  such  as  land,  painting,  i 
plumbing,  glazmg,  <fcc. 

SOLID  MEASURE. 

1  Solid  Foot, 
n28  Inches ^^^^^••;:;;;;;:i  Yard,  or  load  of  earth. 

40  Fre^orrVundtimbVr;y;;..is...,l  Ton  or  Load. 
O,50Feeto.hewnt..be.5  ^^  ^^^^,,,^  ,„a  3 

108  Solid  Feet  i.  ^-^l/f^- ^^^^^^^^  broa^"  and  3  feet 

aeen  or,  commonly,  14  teei  loug, 
1  in^h  deep,  is  a  stack  of  wood  ^^^^^^  ^^^  4  feet  deep, 

128  Solid  Feet,  i.  e.  8  teet  long, 
is  a  cord  of  wood.  ^^^^.ed  all  t^^ngs  that  have  length, 

By  this  measure  are  measureu         -^  o 

breadth,  and  depth. 

r  «r,.-TnHT«^   AND  MEASURES. 

tegers,  then  divide  the  Sum  ^7  aB^^^^yj  ^^^^  the  Remainder 
^^make  one  of  the  next  g^ef  ^/^^nt  to  the  n-t  superior 
nnder  the  row  added,  and  carry^e  ^  ^^^  ^^.^^  ^^^  ^  ^ 

-  denomination,  continuing  the  same  ^ 

simple  Addition. 

^  MONEY. 


:i.57 
734 

lo9 

798 


\ 


3 

7 
9 

8 


lb. 

152 

272 

303 

255 

173 

635 


(• 

£ 

s 

127 

4 

'.25 

( 
»      1. 

271 

.   ( 

524 

379 

,   t 

215 

r 

•..*jjsu-i*?i.  -—•m%.- 


ADDITION   OF   WBI6HTS. 


29 


MONEY. 

(') 

(•) 

C) 

0 

£ 

8. 

d. 

£ 

s.        d. 

£ 

8. 

d. 

£ 

s. 

d. 

:i57  . 

.   1  .. 

H 

525 

..  2  ..  44 

21  .. 

14  .. 

n 

73  . 

2  .. 

14 

734  . 

.  3  .. 

71 

179 

•  •  O  •  •  0 

75  .. 

16  .. 

0 

25  . 

.  12  .. 

7 

595  . 

5  .. 

3 

250 

..  4  ..  74 

79  .. 

2  .. 

44 

96  . 

.  13  .. 

H 

lo9  .1 

14  .. 

u 

975 

•  •  i)  •  •  04 

57  .. 

16  .. 

H 

76  . 

.  17  .. 

34 

■.J07  . 

.  5  .. 

4 

254 

..  5  ..  7 

2G  .. 

13  .. 

81 

97  . 

14  .. 

U 

798  . 

.  16  .. 

n 

379 

..  4  ..  51 

54  .. 

2  .. 

7 

54  .. 

11  .. 

74 

(•) 

(") 

(") 

n 

£ 

s. 

d. 

£ 

«. 

d. 

£ 

s. 

d. 

£ 

s. 

d. 

127 

. .  4  . . 

n 

261 

..  17 

..  14 

31 

..  1  .. 

n 

27 

1 0 

9   5i 

525 

•  •  0   •  • 

5 

379 

..  13 

..  5 

75 

..  13  .. 

1 

16 

..  12  . 

.  94 

271 

..  0  .. 

5 

257 

..  16 

..  7| 

39 

..  19  .. 

74 

9 

..  13  . 

.  3i 

524 

..  9  .. 

1 

134 

..  13 

..  5 

97 

..  17  .. 

34 

15 

..  2  . 

.  7i 

379 

. .  4  . . 

H 

725 

..  2 

..  34 

36 

..  13  .. 

5 

37 

..  19  . 

.  1 

215 

•  •    0         9    9 

81 

359 

..  6 

..  5 

24 

..  16  .. 

34 

56 

..  19  . 

.  11 

TROY  WEIGHT. 


(») 

0 

0 

oz. 

dwt.   gr. 

lb.   oz.   dwt. 

lb. 

oz.   dwt.  gr. 

^ ' 

.  11  ..  4 

7  ..  1  ..  2 

5  . 

.  2  ..  15  .."22 

% 

.  19  ..  21 

3  ..  2  ..  17 

3  .. 

11  ..  17  ..  14 

3 

..  15  ..  14 

5  ..  1  ..  15 

3  . 

.  7  ..  15  ..  19 

7 

. .  19  . .  22 

7  ..  10  ..  11 

9  . 

.  1  ..  13  ..  21 

9 

..  18  ..  15 

2  ..  7  ..  13 

3  . 

9  ..  7  ..  23 

8 

.  13  ..  12 

3  ..  11  ..  16 

5  . 

2  ..  15  ..  17 

..  r4 
..  74 

..  31 


{') 

lb. 

oz. 

dr. 

152 

..  15 

..  15 

272 

..  14 

..  10 

303 

..  15 

..  11 

255 
173 
635 


10 


13 


13 


[RD 

UPOIS  WEIGHT. 

(•) 

(•) 

cwt. 

qrg.   lb. 

t. 

cwt. 

qrs.   lb. 

25 

..  1  ..  17 

7 

..  17 

. .  2  ..  12 

72 

. .  3  ..  26 

5 

..  5 

..  3  ..  14 

54 

..  1  ..  16 

2 

..  4 

..  1  ..  17 

24  ..    1    ..   16 


17 
55 


0 


C3 


19 
16 


3    ..  18   ..   2  ..    19 


^^*    ,.,.,«.*«Mf  ,*^:,^- 


,--1?-:'%«- 


30 


ADDITION   OF   MBASUBES. 

APOTHECARIES'  WEIGHT. 


lb. 

n 

9 

9 

37 
49 


tiCV. 

..    1 
..    2 
..    2 
..    1 
..    2 
..    0 

10  ..    T 
5    ..    2 

11  ..    1 
5    ..    « 

10   ..    5 
0    ..    T 

Fl.K. 
121 
15 
231 
52 
316 
191 


O 


qr. 

2 

1 

0 

1 

2 


n. 


2 

3 
1 
3 


o 

dr. 
,  1 

,  1 
.  2 
1 
5 
4 


scr. 

gir. 

0 

..    12 

1 

..  n 

0 

..  I't 

1 

..    10 

,    2 

..    13 

CLOTH  MEASURE. 


yd 


C) 
qr. 


n. 


135  ..  3 
10  ..  2 
95  ..  3 

116  ..  1 
26  ..  0 

219  ..  2 


2 
0 
3 


(•) 

E.E. 

qr. 

212 

..    2 

152 

..    1 

19 

..    0 

156 

..    2 

19 

..    3 

154 

..    2 

\n. 


1 

2 

1 

0 
1 
1 


55 

81 
55 


yd- 

225 

111 
52 
391 
1.54 
.131 


O 

feet 

.  1 

.  0 

o 

■  '^ 

,.  0 
..  2 
..  1 


LONG  MEASURE. 


in. 

bar. 

9 
3 
3 

..  1 
..    2 

..    2 

10 
1 
4 

..  1 
..  2 
..    1 

0 


ea. 

m. 

12 

..  2 

21 
35 

19 

..   1 
..    2 
..    0 

51 

12 

..    0 

fur. 

po 

1 

..    19 

1 

..    22 

5 

..    31 

6 

..    12 

6 

..  n 

.    5 

..    21 

0) 

r. 


31 


126    ..     -    -         - 
219    ..    2    ••    \> 

S^    ..    14 


LAND  MEASURE. 


O 


a. 
1232 
321 

131 
1219 

459 


', 

P 

1 

..    14 

0 

..    l'-> 

2 

..    !•> 

1 

..    18 

o 

..    11 

ussaam 


ADDITION    OF   MEASURES. 


k 


13 

18 


hhds.  gala  qts. 
31  ..  57  ..  1 
97  ..  18  ..  2 

76  ..  .13  ..  1 

55  ..  46  ..  2 

87  ..  38  ..  3 

55  ..  17  ..  1 


WINE  MEASURE. 


(*) 


,  t. 

hhds 

gals. 

qts 

14 

..  3 

..  27 

..  2 

19 

..  2 

..  56 

..  3 

17 

..  0 

..  39 

..  3 

79 

..  2 

..  16 

..  1 

54 

..  1 

..  19 

..  2 

97 

..  3 

..  54 

..  3 

2 

1 

0 
1 
1 


ALE  AND  BEER  MEASURE. 


A.B.     fir.     gal. 
25  ..  2  ..  7 
17  ..  3  ..  5 
90  ..  2  ..  6 

75  ..   I    ..  't 

96  ..  3   ..  7 

75  ..  0  ..  5 


0) 


B.B. 

fir. 

gal. 

37 

..  2 

..  8 

54 

..  1 

..  7 

97 

..  3 

..  8 

78 

..  2 

..  5 

47 

..  0 

..  7 

35   ..  2  ..  5 


u£j»                                                             ■] 

1* 

O          1 

'M 

hds.  gals.  qts.         | 

76  ..  51  ..  2          W 

57  ..  3  ..  3          1 

97  ..  27  ..  3          1 

22  ..  17  ..  2          1 

32  ..  19  ..  3          1 

55  ..  38  ..  3          1 

19 
;  22 
.  31 
.    12 

.  n 

.    21 


ch.      bu.  pUs. 

75  ..     2  ..  1 

41   ..  24  ..  1 

29  ..  16  ..  I 

70   ..   13  ..  2 

54  ..   17  ..   3 

79   ..   25   ..   1 


DRY  MEASURE.  A 

last.    wey.     q.     bu.    pks. 

38  ..  1  ..  4  ..  5  ..  3 

47  ..   1   ..  3  ..  6  ..  2 

62  ..  0  ..  2  ..  4  ..  3 

45  ..   1   ••  4  ..  3  ..  3 

78   ..   1   ..   1  ••   2  ..  2 
29   ..   1   ..   3  ..   6   ..  2 


P- 

1 

..  14 

0 

..  iv> 

2 

..  !•> 

1 

..  18 

o 

..  17 

{') 

w. 

d. 

71 

. .  3  . 

51 

«.  2   e 

76 
95 
79 


0 


h. 
11 
9 
21 
21 
15 


TIME. 


(') 

w. 

d. 

h. 

07 

..  2  .. 

15  . 

j5 

•  .  o  .  . 

21  . 

7(> 

. .  0  . . 

1  r. 

53 

98 


m. 


r» 


t       M      t   • 


21 

18 


.  42   ..  41 

.  27  ..  51 
.  37  ..  28 
.  42 

.   47 


A\  a. 


f-/ 


aii*«P9ft**r 


) 


32 


ADDITION. 


THE    APPLICATION. 


1.  A  man  was  bom  in  the  year  1750,  when  will  I'^te  f^  y,^*" 

"^  Tl  B  C  and  D,  went  partners  in  the  purchase  of  a  quanU- 
tity'of  goods  A  laid  out  £7,  half-a-g«inea  and  a  crown;  B. 
Tic,  54s;ca.-,  and  D,  87d.     What  w>.  >a>d^o"y-l'»  ._  3.  * 

2er  r^ds^talt^a-gnin'o.  and  a  ^^J^^ t" 

•''fwhat  i;.the  estate  worth  per  annum  when  U.e  t^xes  are 
21  guineas,  the  neat  income  8  score,  £19  :  U  .^^  ^^^^  _  ^^ 

K   Thpre  are  three  numbers;  the  first  is  215,  the  second  519, 
and  tSdl  t'much  as  the  other  two.    What  .^the  ..mot 

"T  Bolht  a  parcel  of  goods,  for  which  I  paid  £54  :  17,  for 
packing  ll'sd/carriage  ll  :  5  :  4,  and  spent  about  the  bargain 
14s.  3d.    What  do  these  goods  stand  mo  m  !^^^  £5,,  .  jo  :  3. 

7  There  are  two  numbers,  the  least  whereof  is  40,  tlieir  Sii- 
ference  14!  I  desire  to  know  what  is  the  greater  nmnber,  and 
the  sum  of  both  ?  ^^^  ^^  ^^^^^  ^^^^^^  g^  ^„^ 

8.  A  gentleman  left  his  elder  daughter  £1500  more  than  the 
vouno-er  and  her  fortune  was  11  thousand,  11  hnudred  and  £11. 
'mafw'rtt  elder  sister's  fortune  and  what  d  d  the  father  leave 
.,     ,,  •  ^ns.  Eldest  sister's  fortune,  £13611. 

""''" '  Father  loft  them  £25722. 

'     9.  A  nobleman,  before  he  went  out  of  town,  ^va.s  teirous  of 
paying  all  his  tradesmen's  bills,  and  upon  mquny,  he  found  that 
he  o^vid  82  guineas  for  rent;  to  Ins  wme  merchant  £72     o  .  0 
to  his  confecSonc.r,  £12  :  13  :  4;  to  h,s  draper  f«^  13    2    to 
his  tailor,  £110  ;  15  :  6;  to  Ins  coach-maker,  £157  .80    to  his 
tallow-chandler,  £8  :  17  =.9;  to  Ins  corn-chandler,  £170  .  6    8 
. ,    to  his  brewer,  £52  :  17  :  0;  to  ms  Duiciier,  ^...^.y^.  '-  _--■ 

■"  mXHJ^^t.:^^^:^  le^hf  t^f  oie'wJn 
f^^  to  the  above  suL  £100,  whicW'J  -^•'f,,*^  3^' 


10.  A 

year,  and 
between 
days;  bel 
15  days; 
and  25  c 
days  old, 

.11.  A 
811  accou 
£150  :  li 
half-crowi 
15  :  9^,  J 
whole  air 

12.  A 

twenty  di 
ing  408 
dwts. ;  si 
knives  ai 
tankard, 
lamp,  w( 
small  art 
weight  oi 

13.  A 

weighed 
the  thirc 
the  fifth, 
pockets, 
the  whol 

'    14.  A 

in  JanuE 
bruary, 
for  good 
May,  £1 
but  tiio 
the  dem 
only  £2' 
vear's  bi 


^i<S? 


'-«<. 


ADDITION. 


88 


take 


10.  A  father  was  24  years  of  age  (allowing  13  months  to  a 
year,  and  28  days  to  a  month)  when  his  first  child  was  born ; 
between  the  eldest  and  next  born  was  1  year,  11  months,  14 
days;  between  the  second  and  third  were  2  years,  1  month,  and 
15  days;  between  the  third  and  fourth  were  2  years,  10  months, 
and  25  days;  when  the  fourth  was  2*7  years,  9  months,  and  12 
days  old,  how  old  was  the  father  ? 

Ans.  58  years,  7  months,  10  days. 

.11.  A  banker^s  clerk  having  been  out  with  bills,  brings  home 
811  account,  that  A  paid  him  £7:5:2,  B  £15  :  18  :  6^,  C 
£150  :  13  :  2^,  D  £1*7  :  6  :  8,  E  5  guineas,  2  crown  pieces,  4 
half-crowns,  and  4s.  2d.,  F  paid  him  only  twenty  groats,  G  £76  : 
15  :  9^,  and  H  £121  :  12  :  4d.  I  desire  to  know  how  much  the 
whole  amounted  to,  that  he  had  to  pay  ? 

Ans.  £396  :  1  :  6i. 

12.  A  nobleman  hiad  a  service  of  plate,  which  consisted  of 
twenty  dishes,  weighing  203  oz.  8  dwts. ;  thirty-six  plates,  weigh- 
ing 408  oz.  9  dwts.;  five  dozen  of  spoons,  weighing  112  oz.  8 
dwts. ;  six  salts,  and  six  pepper  boxes,  weighing  71  oz.  7  dwts. ; 
knives  and  forks,  weighing  73  oz.  5  dwts.;  two  large  cups,  a 
tankard,  and  a  mug,  weighing  121  oz.  4  dwts. ;  a  tea-kettle  and 
lamp,  weighing  131  oz.  7  dwt<». ;  together  with  sundry  other 
small  articles,  weighing  105  oz.  6  dwts.  I  desire  to  know  the 
weight  of  the  whole  2 

Ans.  102  lb.  2  oz.  13  dwts. 

13.  A  hop-merchant  buys  five  bags  of  hops,  of  which  the  fii-st 
weighed  2  cwt.  3  qrs.  13  lb.;  the  second,  2  cwt.  2  qrs.  11  lb.; 
the  third,  2  cwt  3  qrs.  5  lb.;  the  fourth,  2  cwt>  3  qrs.  12  lb.; 
the  fifth,  2  cwt.  3  qrs.  15  lb.  Besides  these,  he  purchased  two 
pockets,  each  weighing  84  lb.  I  desire  to  know  the  weight  of 
the  whole  ? 

Ans.  15  cwt.  2  qre. 

14.  A,  of  Vienna,  owes  to  B,  of  Liverpool,  for  goods  received 
in  January,  the  sum  of  £103  :  12  :  2;  for  goods  received  in  Fe- 
bruary, £93  :  3  :  4;  for  goods  received  in  March,  .£121  :  17: 
for  goods  received  in  April,  £142  :  15  :  4 ;  for  goods  received  in 
May,  £171  :  15  :  10 ;  for  goods  received  in  June,  £142  :  12  :  6 ; 
hilt,  tiirt  iHttPT'  siY  mnn<lis  of  thft  vPiar.  owinn*  to  tha  fallino*  off  in 
the  demands  for  the  articles  in  which  he  dealt,  the  amount  wa^ 
only  £205  :  7  :  2.  I  desire  to  know  the  amount  of  the  wlj^f  ^/ 
vear's  bill  ? 

*  Ans.  £981  '..P 


34 


gUBTRACTIOK. 


SUBTRACnON  OF  MONEY,  WEIGHTS  &  MEASURES. 
Rule     Subtract  as  in  Integers ;  only  when  any  of  the  lower 

denomLtions  are  greater  than  the  .-PP-V^'Tto'thTuLer 
tLi  as  make  one  of  the  next  superior,  adding  it  to  the  upper, 
tm  whTch  take  the  lower;  set  down  the  ditference,  and  carry 
itothe  next  higher  denomination  from  what  you  borrowed. 
Proof.     As  in  Integer. 


MOiNEY. 


£ 
Borrowed  715 
Paid  476 


0) 

8. 

2 
3 


d. 

8k 


£         s.       a. 
Lent  316  . .  3  . .  5i 
Received  218  ..  2  ..   1| 


Remains  to  pay  238 
Proof  715 


18 


loi 

n 


£ 

87  . 
79  . 


8. 

.   2 
.  3 


d.      £        »•         «■ 

10        3  ..  15  ..    li 
7i       1   ..  U  ..    7 


o 

(•) 

£           8. 

d. 

£            8. 

d. 

25  ..    2  .. 

5i 

37   • •    3   .  • 

4i 

17  ..    9  .. 

8i 

25  ..    5  .. 

2i 

£         s.        d.      £ 

321   ..   17   ..   U      59   • 
257    ..   14  ..   7        36   . 


C\  (")  ^"'> 

V         d  £         s.  d.  £         «.  d. 

15  ..   3i  71  ..     2  ..  4  527   ..  3   ..  5i 

17  ..  2  19  ..   13   ..  75  139   ..   5  ..  H 


Borrowed  25107 


s. 
15 


d. 

7 


375  .. 

5 

..  54 

Paid  259  . . 

2 

..  nk 

at  359  . . 

13 

..  u 

different  523  .. 

17 

..   3 

times  274  . . 

15 

..  74 

325  .. 

13 

..  a 

£  8.        d. 

Lent  250156  ..  1  ..  6 

271   ..  13  ..  74 

Received  359  ..  15  ..  3 

at  475  . .  13  . .  9i 

several  527   . .  15  . .  34 

Davments  272  ..  16  ..  5 


Paid  in  all 
^^^ns  to  pay 

'%7 


(")  Bongh 
Sol 


29  .. 


lb. 

(«)   5 

2 


Fl.E. 
(»)   35  . 
17  . 


yds. 

(»)  107  . 

78  . 


a. 
(»)  175  . 
59  . 


SUBTRACTION. 

TROY  WEIGHT. 

lb.       02.     dwt.     gr.  lb.      oz.     dwt.     gr. 

(")     Bought  52  . .   1   . .     7   . .  2  (*)      7  . .  2  . .  2  . .  7 

Sold  39  . .  0  . .  15  . .  7  5  . .  7   . .   1   . .  5 

Unsold 

AVOIRDUPOIS  WEIGHT.     '' 

lb.       oz.      dr.  cwt.     qrs.      lb.  t      cwt.     qrs.     lb 

(»)     35   ..   10  ..  5  («)       35  ..    1   ..   21         (»)    21   ..    1    ..   2  ..   7 

29  ..  12  ..  7  25  ..   I   ..   10  9  ..   1   ..   3   ..  5 

APOTHECARIES  WEIGHT. 

lb.     oz.      dr.    scr.  -'  lb.      oz.     dr.    scr.      gr 

(»)      5  ,.  2  ,.   J    .«  0  (•)     9  ,.   7  ..  2  ..   1   ..  IS 

2..5..2..1  6..7..3..1..1g 


Fl.E.    qr.     n. 

(>)       35  ..  2  ..  2 

17  ..  2  ..   1 


CLOTH  MEASURE. 

yd.      qr.      n. 
(«)     71   ..  1  ..  2 


E.E.    qr,      n. 

(»)      35  ..  2  ..   1 

14  ..   3  ..  2 


LONG  MEASURE. 


yds.       ft.       in. 

bar. 

(>)     107  ..  2  ..   10 

..   1 

78  ..  2  ..   11 

..  2 

lea.      mi.    fur.     po. 

0)    147  ..  2  ..  6  ..  29 

58  ..   2  ..   7  ..  33 


a.        r.        T). 
(»)    175  ..  1  ..  27 

59  ..  0  ..  27 


LAND  MEASURE. 


a.        r. 

(•)    325  ,.  2 

279  ..  3 


.,-^,,, 


■^"xm^A 


36 


SUBTRACTION. 


WINE  MEASURE. 


hhd.      gal,     qts.     pt. 

(')      47  ..  47  ..  2  ..   1 

28  ..  59  ..  3   ..  0 


tun.     hhd.     gal.     qt. 
O      42   ..  2  ..   37   ..  2 
17   ..  3  ..  49  ..  3 


5.  Wha 
to  £305  ? 


6.  A  he 
much  doe 


i,  my 

i 


ALE  AND  BEER  MEASURE. 


A.B.     fir.     gal. 
C)      25  ..  1   ..  2 
21   ..  1   ..  5 


B.B.     fir.    gal. 
O      37  ..  2  ..   1 
25  ..   1   ..   7 


hhd.      gal.      qt. 
C)      27  ..  27  ..   1 
12  ..  50  ..  2 


DRY  MEASURE. 


qu.      bu.      p. 

(»)     72   ..  1   ..  2 

ou   •  t  2   « •   3 

qu.      bu.      p. 

(')     65  ..  2  ..   1 

57  ..  2  ..  3 

• 

ch.      bu.      p. 

O     79  ..  3  ..  0 

54  ..  7  ..  1 


TIME. 


yr8.     mo.    w.     ds. 

(*)      79  ..  8  ..  2  ..  4 

23  ..  9  ..  3  ..  5 


ho.      min.      " 
(»)     24  ..  42  ..  45 
19  ..  53  ..  47 


THE    APPLICATION. 

.  1.  A  man  was  born  in  the  year  1723,  what  was  his  age  in  the  year  1781  ? 

*  Ans.  58. 

2.  What  is  the  difference  between  the  age  of  a  man  born  in  1710,  and 
another  born  in  1766  ? 

w?n».  56. 

3.  A  Merchant  had  five  debtors,  A,  B,  C,  D,  and  E,  who  together  owed 
ip  £1156  ;  B,  C,  D,  and  E,  owed  him  £737.     What  was  A's  debt  > 

Xt  Ana.  £419, 

estate  of  £300  per  annum,  is  reduced,  on  the  paying  of  taxes 


£14:6.    What  is  the  tax  ? 


'SSCi^.SKrSl 


Ans.  £45  :  14. 


7.  A  m 
commodit 
year,  by  c 
months'  ei 


8.  A  ge 
who  was  t 
elder  siste 

9.  A  tri 
gether,  an 
5:2;  to 
£143  :  12 
and  that  h 
£21 :  10 : 
hands,  I  < 
much  i 

ir 

10.  My 
count  of  rr 
Beeswax, 
11  :6;  lin 
the  same  i 
wines  to  t 
£19 : 17  : 
15  :  6.  I 
the  debtor 


MULTI 

Rule.— 

the  produ( 
iiiainder, 

It  the  g; 
multiplied 
multipliefl 
line  by  as 


COMPOUND    MULTIPLICATION,      f 


87 


3.  What  is  the  difference  between  £9154,  and  the  amount  of  X754  added 
to  £305  ? 

^m.  £8095. 

0.  A  horse  in  his  furniture  is  worth  £37  :  5 ;  out  of  it,  11  guineas ;  how 
much  does  the  price  of  the  furniture  exceed  that  of  the  horse  ? 

^ns.  £7  :  17. 

7.  A  merchant  at  his  out-setting  in  trade,  owed  £7r)0;  he  had  in  cash, 
commodities,  the  stocks,  and  good  debts,  £12510  :  7;  he  cleared,  the  first 
year,  by  commerce,  £452  :  3  :  0 ;  wliat  is  the  neat  balance  at  the  twelve 
months'  end  ? 

Ans.  £12212  :  10  :  6. 

8.  A  gentleman  dying,  left  £45247  between  two  daughters,  the  younger 
who  was  to  have  15  thousand,  15  hundred,  and  twice  £15.  What  was  the 
elder  sister's  fortune  ? 

jI/w.  £28717. 

9.  A  tradesman  happening  to  fail  in  business,  called  all  his  creditors  to* 
gether,  and  found  he  owed  to  A,  £63  :  7  :  6 ;  to  B,  £105  :  10 ;  to  C,  £34 : 
5  :  2 ;  to  D,  £28  :  16  :  5 ;  to  E,  £14  i  15  :  8 ;  to  F,  £112  :  U ;  and  to  G, 
£143  :  12  :  9.  His  creditors  found  the  value  of  his  stock  to  be  £212  :  6, 
and  that  he  had  owing  to  him,  in  good  book  debts,  £112  :  8  :  3,  besides 
£21 :  10 :  5  money  in  hand.  As  his  creditors  took  all  his  effects  into  their 
hands,  I  desire  to  know  whether  they  were  losers  or  gainers,  and  how 
much  ? 

it.  Arts,  The  creditors  lost  £146  :  11  :  10. 

10.  My  correspondent  at  Seville,  in  Spain,  sends  me  the  following  ac- 
count of  money  received,  at  different  sales,  for  goods  sent  him  by  me,  viz : 
Beeswax,  to  the  value  of  £37  :  15  :  4;  stockings,  £37  :  G  :  7;  tobacco,  £125: 
11:6;  linen  cloth,  £112:14:8;  tin,  £115  :  10  :  5.  My  correspondent,  at 
the  same  time,  informs  me,  that  he  has  shipped,  agreea<)ly  to  my  order, 
wines  to  the  value  of  £250  :  15;  fruit  to  the  value  of  £51  :  12  :  6;  figs, 
£19  :  17  :  6;  oil,  £19  :  12  :  4;  and  Spanish  wool,  to  the  value  of  £115  : 
15  :  6.  I  desire  to  know  how  the  account  stands  between  us,  and  who  is 
the  debtor  ? 

Ans.  Due  to  my  Spanish  correspondent,  £23  :  14  ;  4. 


MULTIPLICATION  OF  SEVERAL  DENOMINATIONS. 

RuLK. — Multiply  the  first  Denomination  by  the  quantity  given,  divide 
the  product  by  as  many  of  that  as  make  one  of  the  next,  set  down  the  re- 
mainder, and  add  the  quotient  to  the  next  superior,  after  it  is  multiplied. 

If  the  given  quantity  is  above  12,  multiply  by  any  two  numbers,  which 
multiplied  together  will  make  the  same  nuinbpr ;  but  if  no  two  numbaf 
multiplied  together  will  make  the  exact  nvnnber,  then  multiply  thtt|^^         f^ 
line  by  as  many  as  ia  wanting,  adding  it  to  the  last  product,  yi  ^[r^ 


D 


-V-A.. 


38 


/ 


7 


Proof. 

By 

Division. 

(') 

O 

£. 

s. 

d. 

£ 

». 

d. 

35 

:12: 

2 

•75: 

13  : 

H 

3 

COMPOUND    MULTIPLICATiaiJf^ 

je  s.    d. 

62  :  5  :  4i 

4 


£    «.     <2. 

57  :  2  :  44 
5 


71  :    5  :  2i 

• 

0 

1.     18  yards  of  clot 
per  yard. 

li,  at  98.  6d. 
9 

4:    5:6 
2 

2.    26  lb,  of  tea,  at  £1  :  2  :  6 
per  lb.                               8 

8X2=18 

8X3X     — 'SO 

9:0:0 

3 

8  :  11  :  0 

27  :  0  :  0 
Top  line  X2=2  :  5  :  0 

29  :  5  :  0 

3.  21  ells  of  Holland,  at  la.  S^d.  per  ell. 

Faxiit,  £8:1:  IQi 

4.  35  firkins  of  butter,  at  15s.  3|d.  per  firkin. 

Facit,  £2Q  :  16  :  2^. 

5.  15  lb.  of  nutmegs,  at  Is.  2|d.  per  lb. 

Facit,  £27  :  2  :  2^. 

6.  37  yards  of  tabby,  at  9s.  7d.  per  yard. 

^  Facit,  £17  :  14  :  7. 

7.  97  cwt.  of  cheese,  at  £l  :  5  :  3  per  cwt. 

Facit,  £122  :  9  :  3. 

8.  43  dozen  of  candles,  at  6s.  4d.  per  dozen. 

Facit,  £13  :  12  :  4. 

9.  127  lb.  of  Bohea  tea,  at  12s.  3d.  per  lb. 

Facit,  £77  :  15  :  9. 

10.  135  gallons  of  rum,  at  7s.  5d.  per  gallon.  • 

^  Faxjit,  £50  :  1  :  3. 

11.  74  ells  of  diaper,  at  Is.  4^d.  per  ell. 

^  .  Facit,  £5  :  1 :  9. 

12.  6  dozen  pair  of  gloves,  at  Is.  lOd.  per  pair. 

^  Facit,  £6  :  12. 

the  given  quantity  consists  oi  f ,  §,  yr  4. 

Divide  the  given  price  (or  the  price  of  one)  by  4  for  i,  by  2  fpr 
IT  4,  first  divide  by  2  for  h,  then  divide  that  quotient  by  2  for  i,  add 
>e  product^  and  their  sum  will  be  the- answer  required. 


J 


13. 


:* 


14. 
16. 

16.  ; 

17.  \ 
,  18.  ( 

30.  1 
21.  1 

00     o 

Wa4«       O 

23.  2 

24.  1 

25.  3' 

26.  5( 

27.  9( 


W»iMwI»^>pl»Mi'-n^ 


:2i 

6 
8 

:0 

.0 
3 

:0 
:5 

:0 
:0 

:5 

:0 

# 


.     ,i. 


^ 


J. 


***** 


5j||  COMPOUND   MULTIPLICATIOIf. 

13.  25^  ells  of  holland,  at  3  :  4|d.  per  ell. 

5       5X5=25 

16:10^    ■ 
6 


39 


4:4:4^  =  25 

4:6:01  =  251 

14.  I5i  ells  of  diaper,  at  Is.  3d.  per  ell. 

15.  m  ells  of  damask,  at  4s,  k  per  ell.  ^''^*'  ^'  ''  ''  '''^' 

16.  35 J  ells  of  dowlas,  at  Is.  4d.  per  ell.   ^'"*'  ^' '  '  =  ''^• 

17.  n  cwt.  of  Malaga  raisins,  at  £l :  1 :  6  pe!l\^'  '  ^  ^  ^' 
.  18.  6f  .barrels  of  herrings,  at  £3  :  15  :  7  Sar^Ii;  ''  ''  ''^' 

^  19.  35^  cwt.  doubled  refined  sugar,  at  £4^^^:^ peV  cU'^' 

^0.  15H  cwt.  of  tobacco,  at  £4:17:  lO^f  cwt ''  '''''''' 

Qi    n'7i.  «.„n         i?         ,  Facit,  £755 :  15 : 3. 

il.  117i  gallons  of  arrack,  at  128.  6d.  per  gallon. 

oo    rks  ^^4.    i?    1  Facit,  £73  :  5 :  7*. 

-2.  85f  cwt.  of  cheese,  at  £1 :  7  :  8  per  cwt. 

^<J.  29i  lb.  of  fine  hyson  tea,  at  £l  :  3  :  6  per  lb. 

24.  171  yards  of  superfine  scarlet  drab,  at  i":  sfe'per  yar^i 

25.  37^  yards  of  rich  brocaded  silk,  at'l2!:td.  per  yarV  '*' 

26.  56^  cwt.  of  sugar,  at  £2  :  18  :  7  per  cwf '*'  ^'''''''  '' 

9n    n«i  «„.+    c  .         «  *'^c^<^»  £166 : 4 :  74. 

27.  96^  cwt.  of  currants,  at  £2  :  15  :  6  per  cwt. 

iJefladme  silk,  at  18s.  Cd.  per  lb.  ,A 


wheat,  at  4s.  3d.  per  bushel 


P'acit,  £42  :  6  :  4^;(vf 


r 

^f:- 
% 


d2 


Facit,  £18 


,/ 


,<»>'.• 


~n 


40 


.     COMPOWB   MWTIPUCATIOH. 


i 


30.  120J  cwt.  of  hops,  at  £4  .  T  •  »  >    ^^^j^^  £528  :  6  :  1i- 

31.  401  yards  of  cloth,  at  3s.  9|d.  per  yard^^  ^^^  .  ^  .  24. 

32.  729  ells  of  cloth,  at  Is.  H^-  pe'  «"•  j,^;^^  £217  :  3  :  6*. 

33.  2068  yards  of  lace,  at  9s.  Sid.  per  yard.  ^^^^  _  ^^  .  ^^ 

THE    APPLICATION. 

..Whats„.ofn,oney.J^..e..deda.oo^tl8.enso 

tiiat  each  man  may  receive  £U  .  b  .  «t  •       ^^^  ^^SS  :  0:9. 

*    V  ^  iirize   which  amounted  tc 
2   A  prWateer  of  250  men  to^\  M^^^^'  ^     ^  ,^,     ize  1 
£125    15  :  6  to  each  man;  w^^t.^^^%;7£3l443  :  15  :  0.^ 

.    Wtnt  difference  is  there  between  t^v,ce  eight  ana      y, 
Joe5-gHand«hatisthe.rproduct^^^.^_,^^,p    auot. 

X.       tW 'oreater  of  them  is  37  times 
5   nere  are  two  nutnhers,  *e  greater  ^^^    ,,oduct  are 

«%  their  difference  19  Sr3254tum,%e«a  Jproduc. 

Tth    sum  of  two  numbers  ^^^^  X^ 
what  is  their  product  and  the  'q"^'-^^  ^^^^  ^f  their  difference. 
Ani  31104  Product,  f  ^^^^ons  of  horse,  each  157 
1.  In  an  army  consistmg  ot  187  »V"«'  effective  sol- 

J„,  and  207  ba^t^Uon.  -l^.^XthCa^  *"  sill 
diers,  supposing  that  in  i  nost^^**  ^^s^  144800. 

*  •,«,;«  finwrv  with  his 

8.  What  sum  did  that  geutW  r^ive J  do  J^^ 
wife  whyje  fortune  was  her  wedamg  smt  ,J      1     .^  ^^^^  q„,„ 
IJ^o'rows  of  furbelows,  each  tarbelow  87  qmlls,  ^^^_^^  _  ^^  .  ,^^ 

"rr*:Lanthad  £19118  to  begin  trade  with -^f^J^y;* 

.^^etter  he  deHred  £1086  » J-^j-Jfa^T^^^*  ^was'^in  trade,  he 

■     y<''«;^»^'■^^'!!'riwnother,£475:4:6/ 


t 


ne  to 


'lose,  one  year  with  another, 


end? 


ds  realfortune  at  12  ycars^ena^^^^^^  .  g 


f 


/% 


:/) 


). 


1,  so 


9. 

d  tc 
\ 

0. 
lalf  a 


08. 


^,  and 


I 


uct. 
timeB 
ict  are 
luct. 
,   144; 

ence. 
icb  15^ 
Ave  sol- 

4806. 
^ith  his 
,  having 
ich  quill 
L4  :  0. 
•  5  yeapa 
ade  2.:o6d 
trade,  he    , 
:  4  *.  6/  -f 

;  8 :/       ; 


.y  COMPOUND   MULTIPi^ICATION. 

10.  In  some  parts  of  the  kingdom,  they  weigh  their  coals\ 
machine  in  the  nature  of  a  steel-yard,  waggon   and  all.     Ti, 
of  these  draughts  together  amount  to  137  cwt.  2  qrs.  10  lb.,  \ 
the  tare  or  weight  of  the  waggon  is  13  cwt.  1  qr.;  how  mai 
coals  had  the  customer  in  12  such  draughts  ? 

Ans.  391  cwt.  1  qr.  12  lb. 

11.  A  certain  gentleman  lays  up  every  year  £294  :  12  :  6, 
and  spends  daily  £l  :  12  :  6.  I  desire  to  know  what  is  his  an- 
nual income  ?  •^^«-  ^887  :  15  :  0. 

12.  A  tradesman  gave  his  daughter,  as  a  marriage  portion,  a 
•scrutoire,  in   wl:ich  there  were  twelve  drawei-s,  in  each  drawer 

were  six  divisions,  in  each  division  there  were  £50,  four  crown 
pieces,  and  eight  half-crown  pieces;  how  much  had  she  to  her 
fortune?  Jns.  £3744. 

13.  Admitting  that  I  pay  eight  guineas  and  half-a-crown  for  a 
quarter's  rent,  and  am  allowed  quarterly  15s.  for  repairs,  what 
does  my  apartment  cost  me  annually,  and'  how  much  in  seven 
years?  Ans.  In  1  year,  £31  :  2.     In  7,  £217  :  14. 

14.  A  robbery  being  committed  on  the  highway,  an  assessment 
was  made  on  a  neighbouring  Hundred.for  the  suni  of  £380  :  15  : 
e,  of  which  four  parishes  paid  each  £37  :  14  :  2,  four  hamlets 
£31  :  4  :  2  each,  and  the  four  townships  £18:12:6  each ;  how 
much  was  the  deficiency?  ■^^^•'  ^^^  •  ^2  •  2. 

15.  A  gentleman,  at  his  decease,  left  his  widow  £4560;  to  a 
public  charity  he  bequeathed  £572  :  10;  to  each  of  his  four  ne- 
phews, £750  :  10;  to  each  of  his  four  nieces,  £375  :  12  :  6;  to 
thirty  poor  housekeepers,  ten  guineas  each,  and  150  guineas  to 
his  executor.  What  sum  must  he  have  been  possessed  of  at  the 
time  of  his  death,  to  answer  all  these  legacies  ?  - 

Ans.  £10109  :  10  :  0. 

16.  Admit  20  to  be  the  remainder  of  a  division  sum,  423  tho 
quotient,  tho  divisor  the  sura  of  both,  and  1^  more,  what  was  the 
number  of  the  dividend?  ^»«-  195446. 

EXAMPLES  OF  WEIGHTS  AND  MEASURES. 

(*)  Multiply  9  lb.  10  oz.  15  dwts.  19  grs.  by  9. 
,,  n  Multiply  23  tons,  0  cwt.  3  qvs.  18  lb.  by  7. 
' .  M  Multiply  107  yards,  3  qrs.  2  nails,  by  10. 


// 


I 


F*y 


'J  t> 


_1-    I. 


^    iliiV.    -J 


Lilt. 


1  1 


Multiply  27  beer  bar.  2  firk.  4  gal.  3  qts.  by  12.         J, 
Multiply 


miles,  6  fur.  26  poles,  by  12, 
u3 


^.P^ 


/' 


c*.-»t*«« 


«MiltlMt«L~' 


^.. 


Z^^m 


*^ 


L 


\: 


DIVISION. 

DIVISION  OF  SEVERAL  DENOMINATIONS. 

Rule.  Divide  the  first  Denomination  on  the  left  hand,  and  if 
any  remains,  multiply  it  by  as  many  of  the  next  less  as  make 
one  of  that,  which  add  to  the  next,  and  divide  as  before. 

Proof.    By  Multiphcation. 


(■)  (')    . 

£      s.    d.  £    s.    a. 

2)25  :    2  :  4(  3)37  :1  :1( 

12  :  11  :  2 


£     s.    a. 
4)57  :  5  :  1( 


£    s.    d. 
6)52  :  1  :  0( 


(')  Divide  £140Y  :  11  :  1  by  243. 
•)  Divide  £700791  :  14  :  4  by  I79i 
'')  Divide  £490981  :  3  :  7^  by  31715, 
')  Divide  £19743052  :  5  :  H  by  214723. 

THE    APPLICATION. 

1.  If  a  man  spends  £257  :  2  :  5  in  twelve  months'  time,  what 
IB  that  per  month  ?  ^^s-  ^21  :  8  :  GJ. 

2.  The  clothing  of  35  charity  boys  came  to  £57  :  3  :  4,  what 
ia  the  expense  of  each?  -^^*^-  ^I  *•  ^^  :  8. 

3.  If  I  gave  £37  :  6  :  4|  for  nine  pieces  of  cloth,  what  did  1 
give  per  piece  ?  Ans.  £4.  :  2  :  11. 

4.  If  20  cwt.  of  tobacco  came  to  £27  :  5  :  4^  at  what  rate 
is  that  per  cwt.  ?  ^w«-  ^^  •  '^  '  ^• 

6.  What  is  the  value  of  one  hogshead  of  beer,  when  120  are 
aold  for  £164  :  17  :  10  ?  ^ns.  £l  :  5  :  9i 

6.  Bought  72  yards  of  cloth  for  £85  :  6  :  0.     I  desire  to  know 
at  what  rate  per  yard  ?  -4ws.  £1:3:  8^. 

7.  Gave  £275  :  3  :  4  for  36  bales  of  cloth,  what  [b  that  for  2 

bajes?  ^*''*- ^^AL^^- 

'\^8.  A  prize  of  £7257  :  3  :  6  is  to  be  equally  diVidSakWongst 

sailoi-s,  what  is  each  man's  share  ? 
^^  Ans.  £14  :  10  :  3^ 

ik\^*?hf>re  ?,Tn  2545  bullocks  to  be  divided  amongst  509  men,  1  u_ 
\.  ^^know  how  many  each  man  had,  and  the  value  of  e»«^;^ ' 
^S^ 'share,  supposing  every  bullock  worth  £9  :  14  :  6.  f'J-' 

4eL.  5  bullocks  each  man,  £48  :  12  :  6  each  share. 


1^ 


:"!Hf>«,*.»^,*.,.>tj^ 


'wKJf  .'■^^>' 


1 


i 


men,  I  jj^ 
of  eJiei^;^ 


DIVISION. 

10.  A  gentleman  has  a  garden   walled  in,  containing  9625 
yards,  the  breadth  was  35  yards,  what  was  the  length  ? 
^  ..  '  Aus.  215. 

11.  A  club  in  London,  consisting  of  25  gentlemen,  joined  for 
a  lottery  ticket  of  £10  value,  which  came  up  a  prize  of  £4000. 
I  desire  to  know  what  each   man  contributed,  and  what  each 

man's  share  came  to  ? 

Ans.  Each  contributed  8s.,  each  share  £160. 

12.  A  trader  cleared  £1156,  equally,  in  17  years,  how  much 
did  he  lay  by  in  a  year  ?  -^w^-  £6 8. 

13.  Another  cleared  £2805  in  1^  years,  what  was  his  yearly 

increase  of  fortune  ? 

Ans.  £374. 

14.  What  number  added  to  the  43d  part  of  4429,  will  raise  it 
U/'.i40?  ^  Ans.  131. 

16.  Divide  20s.  between  A,  B,  and  C,  in  such  sort  that  A  may 
have  2s.  .less  thai  B,  and  C  2s.  more  than  B  ? 

%^,,,     . ,;  Ans.  A  4s.  8d.,  B  6s.  8d.,  C.  8s.  8d. 

tk  If  there  are*  1000  men  to  a  regiment,  and  but  50  officers, 
how  many  privateimen  are  there  to  one  officer  ? 

Ans.  19. 

17.  What  number  is  that,  which  multiplied  by  7847,  wil 
make  the  product  3013248  ?  Ans.  384.  / 

18.  The  quotient  is  1083,  the  divisor  28604,  what  was  the  di- 
vidend if  the  remainder  came  out  1788  ?  t 

Ans.  30979920. 

19.  An  army,  consisting  of  20,000  men,  took  and  plundered 

>a  city  of  £12,000.     What  was   each  man's  share,   the  wholo 

being  equally  divided  among  them  ? 

Ans.  12s. 

20.  My  purse  and  money,  said  Dick  to  Harry,  are  worth  12s. 
8d.,  but  the  money  is  worth  seven  times  the  purse.  What  did 
the  purse  contain?  ^^*;  Us.  Id. 

21.  A  merchant  bought  two  lots  of  tobacco,  which  weiglied 
12  cwt.  3  qrs.  15  lb.,  for  £114  ;  15  :  6.  Their  difference  in 
point  of  weight,  was  1  cwt.  2  qi-s.  13  lb.,  and  of  price,  £7  :  15  ; 
0.     I  desire  to  know  their  respective  weights  and  value  ? 

Ans.  Less  weight,  5  cwt.  2  qrs.  15  lb.     Price,  £o3  :  10. 
Greater  weight,  7  cwt.  1  qr.    Price,  £61:5:6 


/ 


'.     jrnce,  juoi  ;  o  .  u-      y  ^ 

Ji;i,    i/iViUU     iUUU    tJlUtt'iia    in    su-wn    «    Lin-^iiti-.i    f.-.  v --    — -    -1-7   f    j 


(    . 


I 


/v<^     -r^'-.iJ^ 


>^< 


0.  that  A  may  receive  129  more  than  B,  and  B  178  le**'  'Mn  1/ 

Ans.  A  300,  F*    £^r  f iP"^.^ 


Ml^.^^^ 


HWP'- 


/I 


kK' 


BILLS   OF   PAKCEL8. 

EXAMPLES   OP   WEXOHTB   A..   MEAB.BBS. 

2.  Divide  29  to^^' ^%'7,;  Vnails,  by  10. 

3.  Divide  114  yards,  3  qrs  2  "''^;'^'^  J^    n. 

4   Divide  1017  miles,  6  ^^^'^- ^^  ^^^^        26. 
t  Divide  2019  acres,  3  -o^/^3  P^^,^^^^^  days,  11  bours,  27 
6.  Divide  n1  years,  7  montns,  o 
minutes,  by  37. 


BILLS  OF  PARCELS. 
hosiers'. 


S?>  ' 


^.)Mr.Joh„«^^g^^^j^^^^„. 


s.    «?. 


May  1, 18 


4-      4.  *  6  per  pair  ** 
8  Pair  of  worsted  stockings ^^"y.,  oj...... 

5  Pair  of  thread  ditto.. U:0....... 

3  Pair  of  black  silk  ditto ^^  .  ^ 

6  Pair  of  milled  bose -^  ^  .  g 

0,  Pair  of  cotton  ditto i  •  8  per  yard 

^>^Yards  of  fine  flannel ^^2:2 

\ 


MERCERS . 

n  Mr.  Isaac  Grant,  May  3, 18 

^  ^  Bought  of  John  Sims,        ^^    ^ 

at     .  9  ■•  6  per  yard  £ 

15  Yards  of  satin  . . .  •  •  •  • '  *  *  .17  :  4 '• 

18  Yards  of  flowered  sik ^^  .  g 

12  Yards  of  rich  brocade ^  3:2.... 

16  Yards  of  sarsenet ^     g^  ^ . , 

.Q  Y.vds  of  Genoa  velvet a- a..., 

3  Yards  of  lutestring "' 


£62  :  2  : 6 


h  yt«A« Jk  If tp''^'  * 


"%■, 


■•/ 


;#-^ 


BILLS    OF   PARCELS. 


LINEN    DRAPERS  . 


(')  Mr.  Simon  Surety, 

Boufilit  of  Josiah  Short. 


s.    d. 


June  4,  18 


4  Yards  of  cambric at. . .  12  :  6  per  yard  £ 

12  Yards  of  muslin 8  :  3 

1 5  Yards  of  printed  linen 5  :  4 

2  Dozen  of  napkins 2  :  3  eacli  . . . 

14  Ells  of  diaper 1  :  7  per  ell . . 

86  Ells  of  dowlas 1  :  1^ 


£17  :  4 : 6^ 


milliners'. 

(*)  Mrs.  Bright, 

Bought  of  Lucy  Brown. 

£     s.     d. 
18  Yards  of  fine  lace at. .  .0  :  12  :  3  per  yard  £ 

5  Pair  of  fine  kid  gloves 0  :    2  :  2  per  pair 

12  Fans  of  French  mounts 0  :    3:6  each  . . . 

2  Fine  lace  tippets 3  :    3:0 

4  Dozen  Irish  lamb 0  :    1  :  3  per  pair 

6  Seta  of  knots. 0  :    2  :  6  per  set. . 


June  14,  18 


£22  :  4  :  4 


woollen  drapers', 


(*)  Mr.  Thomas  Sage. 

Bought  of  Ellis  Smith. 

£     s. 

17  Yards  of  fine  serge. . .  .at. .  .0  :    3 

1 8  Yards  of  drugget 0  :    9 

15  Yards  of  superfine  scarlet  . .  .1  :    2 

16  ^ardsof  black 0  :  18  :  0 

25  i  'ards  of  shalloon 0 


June  20,  18 

9  per  yard  £ 

0... 

0 


...... 


If   i ';ards  of  Urab 


\ 


i 


1  :9 

.0  :  17  :6 


*Kr 


..c 


y 


A 


iS"^ 


BILLS   OF   PAKCELS. 

leather-sellers'. 


(•)  Mr.  G-^les  H^rris^^^  ^^  ^^^^  ^^,^^, 


July  1,^8 


d. 


W 


,,...3:9perBbu^ 

27  Calf  Skins 1  :  T 

^'   cheepditto ....  1:8 

I'e  Co  uved  ditto •;.V.;..U:6 • 

15  Buck  ditto 10  :^. ; 

17  Russia  Sides 1:2^ _ 

120  Lamb  Skins £38  :  1*^  •  ^ 


I 


0  Mr.  Bic^-^^yof  Francis  Effiot.^      ^ 


July  5, 18 

«igWl5lb.     __'. 0-.    3.._    _^ 


July  6, 18 


M 


[{' 


CHEESEMONGERS  . 

•  at  ..0--6perlb.;fi 

p. .  K.  ^f  htttter,  «t.  28  ID. 0  ;  4 

"•■wA-e  cheeses,  1'^ ;  '"•  •  •;;■....  .0  :  3 ;     ^ 

XUsWre  ditto,  15  \b.  •  •  • 0:6 ^ 

■■  \  f\r<^xc.  cheese "^  .\4 1 


y 


1 


1 

wit 
witll 


'.  i 


7:5 


18 


:  2  :  3i 


iy  6, 18 


M 


\\ 


y 


REDUCTION.  \ 

n  Mr.  Abraham  Doyley,  j  |    20,  18  '* 

^  ^  Bought  of  Isaac  Jones.  Juiy      , 

1   /» 
at  .1  :  10  per  bushel  * 
Tares,  19  bushels ^^3.    g^ 

Pease,  18  bushels '/.*..  25  :    0  per  quarter 

Malt,  7  quarters /.'.'//.  .1  :    5  per  lb. . .  • 

Hops,  15  lb ! !  [2  :    4  per  bushel 

)at8,  6  qrs..... V/.'.4  :    8 

:     ^eans,  12  bushels . 

^  £23  :  7  :  4 

i  •  ,  — - 

\  REDUCTION  PP       y} 

\    hi.  l:    1  :0 

I  IS        inea 0:10:6 

\     viisalf  ditto '.'/..  .1  :    0:0 

\\     \  Sovereign '.  .0  :  10  :  0 

(Wie^  Half  ditto  . . .  • ^  ^  0  :    5:0 

'       U    3\CJrown 0:    2:6 

Vvt8.\Talf  ditto ^^  .    i:0 

J^i.^^^;:^^  T^.^^enr 

haM  v.igh  Crsixp^^^^      fourpence,  threepence,  twopence,  penny, 

/  i      33.  A^ ^^^any  shillmgs  and  pence  ? 
.\    \     y.  of  silv' 
1     j     \  dwts.  A  '  ^, 

A      if\*'^' 'M^hillings.  •      4^p\ 

A|^  jiul^doS  J^^^ 


■»•« 


-T*V»». 


'***''^*^iji»y?ii«iii  i-v 


REDUCTION. 


In  £12,  how  many  shillings,  pence,  and  farthings? 


3.  In  311520  farthings,  how  many 


Ans.  2408.  2880d. 

? 

.    „  ^    , .  Ans.  £324  :  10. 

4.  How  many  farthings  are  there  in  21  guineas  ? 

^    r     n,^  ,    ,  ■^^^-  21168. 

6.  m  i.17^:  6  :  3^,  how  many  farthings  ?  ^n*.  lGo73.   / 

6.  In  £25  :  14  :  1,  how  many  shillings  and  pence? 

^ws.  514s.  6169d. 
/.  m  17940  pence,  how  many  crowns?  Am.  299. 

[|   f  ^-  I"  15  crowns,  how  many  shillings  and  sixpences? 

n    T    rH  •.    ,^  ,  ^W5.  75s.  150  sixpences.  ' 

9.  In  57  half-crowns,  how  many  pence  and  farthings  ? 

^ .    -  ^W5.  1 7 1  Od.  6840  farthings. 

10.  In  52  crowns,  as  many  half-crowns,  shillings,  and    pencvin 
how  many  farthings  ?  ^^  ^  21424./ 
i^ri^'  P'^r   "^^°y   P^'^^^'   shillings,   and   pounds,   ^re   there)'^ 

Tn^TT       "^^-  ^^«-  4320d.  360s.  £18.   ' 

12.  How  many  guiijeas  in  21168  farthino-s  ?  / 

10    T    1     H    i.    1 .  ^4w5.  21  guineas,  ■) 

13.  In  16573  farthings,  how  many  pounds?  v** 

Ans.  £l7  *  5  *  3' 

14.  In  6169  pence,  how  many  shillings  and  pounds  ?' 

15.  m  6840  farthings,  how  many  pence  and  half-crowns  ?  ^ — siiij- 

i«     T     „   ,        »    ,  ^«.  IVlOd.  57  lmlf-cro\)2  52 

16.  in    21424  farthings,  how  many  crowns,  halt-crowni+^  vis « 
hngs,  and  pence,  and  of  each  an  equal  number  ?  Anf^;   Iqs 

17.  How  many  shillings,  crowns,  and  pounds,  in  60  gui^     &    ' 

lo    tj  J        H         .  -4ws.  12608.  252  crowns^     V» 

18.  Keduce  76  moidores  into  shillings  and  pounds?     4y  ^v$[ 

■.o    T^   1        ^  ^««.  2052s.  £11, ,         U:c 

19.  Reduce  £102.:  12  into  shillings  and  n^oidores?  #  Vk 

TT  "^'^^*'  2052s.  76  17 

20.  How  many  shillings,  half-crowns,  and   crowns^' 
lu  i^556,  and  ot  each  an  equal  number  ?  1 

o,    T„ ,.  -^^^6M308  each,  an|. 


1  ir*u5  nair-crowns,  as 
ounds  ? 


many  crowns  and  si 

AnsM. 


vi  men  brought  £15  :  10  each  into  the/^ 
X>,  how  many  must  they  have  in'^0 
',,  Ans.  103  ffu--^ 

*   i 


?\ 


V 


1 1 


-( 


REDUCTION. 


24.  A  certain  person  hnr)  ok  ^  ,  .      •^^'''  ^15  :  10. 

"eas  a  crown,  and  a  1  i.      ?  P"'''''  ^"^  ^"  ^^^^^  P"'^^  12  ir„i. 
.^  ^ .  ^        vn,  and  a  moidore,  how  many  pounds  sterling  had  he 

25.  A  gentleman,  in  his  will  loff  -P^n  .     n  ^^*-  '^^^^• 

tlmt  ^  should  bo  o.  ven  to  Inripnf  "^  *i'^  P^^^'  '^'^^  ^^^^^^ed 

poor  women,  each  to  14  2TTd  ^t"' '"'^  l"  ^'''''  ''-^  to 
1«.--|  to  poor  girls,  each  to  l.^vro^  T'^  ^^^''  ^^^^  ^^  ^^'^ve 
person  wh^  distfibu  ed  it  I  demld  T^'^''  ^'^"^'"^^"^^^  *^  ^^^ 
there  were,  and  what  tlm\J.nnCv''-J  ""^"^  ^^  ^^^^^^  sort 
Wilis  trouble?  Pei^^onwho  distributed  the  money  had 

Ans.  66  men,  100  women  200  boys,  222  girls, 
*^  .  13  .  6  for  the  person's  trouble, 
•  TROY  WEIGHT. 

26.  In  27  ounces  of  gold,  how  many  grains  ? 

27.  In  12960  grains  of  gold,  how  many  ounces?^'''  '''''• 

28.  In  3  lb.  10  oz.  7  dwt..  5  gr.  how  many  grains  ?  ^"''  ''' 

29.  In  8  ino-ots  of  ^llvn^  ^o^i,       •  i  •       ^  ^^*-  22253. 

131.  Bouofht  7  intrntc  r.f  c•,^  1  -^''^'^''  8  mjyots. 

|wf3.  ho,v  many  S       ''™''  ''••'<^''  ~"''»°"ff  23  ib.  s'o^  7 
'  32.  A  gentleman  s^nf  n  +nr.i.„  4^    i  •        ,         ^^*-  945336. 
«0  ....  8  Lfe.  n^^"  o?cl  rod  ±  1'"  ''T  ^f  .^™'«''  «'«'  --ish-l 

!  d«b.  10  .^r.  eacl":  Ll  rf  ""'it  ", ,'"'?  -^"'f-*  -'  "  "^  _ 

I'Or  do;v5^ 


*'|"3oz.  10dwts:e;ich;  and 


1 


doz.  and 


ror  every  tank.-ird  to  h 


forks  of  21 


i.  u\Yt3.  ly  o-r. 


'Jozen  of  forks ;  what^is  the 


'ive  one  salt,  a  d 


oz.  11  dwts.  1 


r.  ifj 


Alls.  2  of  each  sort,  8 


number  of  euch  i">f'5 


',  a  Qozen  .>f:^r;,.  ^fg/ 


v-i 


oz.  9  d\vt' 


z^- 


u  * 


^ 


/*yL  REDUCTION 

V  4 

AVOIRDUPOIS  WEIGHT.  Wi 

Note.— There  are  several  sorts  of  silk  which  are  weighed  by  a  great 
ppund  of  2 1  oz.  others  by  the  common  pound  of  IG  oz. ;  therefore, 

To  bring  great  pounds  into  common,  multiply  by  3,  and  divide  by  2,  ot 
add  one  half 

To  bring  small  pounds  into  great,  multiply  by  2,  and  divide  by  3,  or  sub- 
tract one  third. 

Things  bought  and  sold  by  the  Tale. 

12  Pieces  or  things  make  1  Dozen 

12  Dozen 1  Gross. 

12  Gross,  or  144  doz 1  Great  Gross. 

24  Sheets 1  Quire. 

20  Quires 1  Ream. 

2  Reams 1  Bundle. 

1  Dozen  of  Parchment.  12  Skins. 
12  Skins 1  Roll. 

34.  In  147G9  ounces  how  many  cwt.  ? 

Ans.  8  cwt.  0  qr.  27  lb.  1  oz. 

35.  Reduce  8  cwt.  0  qra.  27  lb.  1  oz.  into  quarters,  pounds,  and  ouncea. 

./Jn*.  32  qrs.  923  lb.  14709  oz. 

36.  Bought  32  bags  of  hops,  each  2  cwt.  1  qr.  14  lb.  and  another  of  150 
lb.  how  many  cwt.  in  the  whole  ? 

Ans.  77  cwt.  1  qr.  10  lb. 

^--^'I.   In  34  ton,  17  cwt.  1  qr.  19  lb.  how  many  pounds  ? 

\  A71S.  78111  lb. 

38.'  In  547  great  pounds,  how  many  common  pounds  ? 

Ans.  820  lb.  8  oz. 

39.  In  27  cwt.  of  raisins  how  many  parcels  of  18  lb.  each  ? 
>  Am.  168. 

;     40.  In  9  cwt.  2  qrs.  14  lb.  of  indigo,  how  many  pounds  ? 

\  Ans.  1078  lb. 

I     41.  Bought  27  bags  of  hops,  each  2  cwt.  1  qr.  15  lb.  and  one  bag  of  137 
»  '  lb.,  ho\\many  cwt.  in  the  whole  ? 

\  Ans.  65  cwt.  2  qrs.  10  lb. 

42.  Hdw  many  pounds  in  27  hogsheads  of  tobacco,  each  weighing  neat 
6S  cwt.  ? 
^  Ans.  26460 

■j»  ^  In  552  common  pounds  of  silk,  how  many  great  pounds  ?  j   ^, 

V     vw    ^  Ans.  36f 

C^  »^N^        '^7  parcels  of  sugar  of  16  lb.  2  oz.  are  there  in  16  cwt.  l/ .  j^ 

vS^  ■•,'■■  '{'") 

^11^  ,^      '■c    ,      .         <?!»,«.  113  parcels,  and  12  lb.  14  oz.  ovcru 


■.V   "r 


\  «■»' 


T        '«f  •*_* 


..7 


REDUCTION. 

/ 

APOTHECARIES'  WEIGHT. 

46.  In  27  lb.  V  oz.  2  dr.  1  scr.  how  many  grains? 

Ans.  169020. 

46.  Hqw  many  lb.  oz.  dr.  scr.  are  there  in  159020  grains? 

Ans.  27  lb.  7  oz.  2  dr.  1  scr. 


CLOTH  MEASURE. 


Ans.  432. 


47.  In  27  yards,  how  many  nails  ? 

48.  In  75  English  ells,  how  many  yards? 

Ans.  93  yards,  3  qrs. 

49.  In  03 1  yards,  how  many  English  ells?  Ann.  76. 

50.  In  24  pieces,  each  containing  32  Flemish  ells,  how  many 
English  ells?  .^l^,?.  460  English  ells,  4  qrs. 

51.  In  17  pieces  of  cloth,  each  27  Flemish  ells,  how  many 
yards?  ^'^**'  ^^^^  yards,  1  qr. 

62.*  Bought  27  pieces  of  English  stuff,  each  27  ells,  how-many 
yards?  -^'^''*-  ^-H  yards,  1  qr. 

63.  In  Olli  yards,  how  many  English  ells? 

•^  Ans.  729. 

54.  In  12  bales  of  cloth,  each  25  pieces,  each  15  English  elK 
how  many  yards  ?  ^^''^-  5625. 

LONG  MEASURE. 

65.  In  57  miles,  how  many  furlongs  and  poles  ? 

Ans.  456  furlongs,  18240  poles. 

66.  In  7  miles,  how  many  feet,  inches,  and  barley-corns  ? 
Ans.  30960  ft.  443520  in.  1330560  b.  corns, 

67.  In  18240  poles,  how  many  furlongs  and  miles? 

Ans.  456  furlongs,  57  miles. 

68.  In  72  leagues,  how  many  yards?  Ans.  380160. 

69.  In  380160  yards,  how  many  miles  and  leagues! 

Ans.  216  miles,  72  Iciigues. 

60.  If  from  London  to  York'  be  accounted  50  leagues,  I  de-   j;j 
mand  how  many  miles,  yards,  feet,  inches,  and  barley-corns  ?         ^ch^ 
Ans.  150  miles,  264000  yards,  792000  feet        ^ 
.^,  9504000  inches,  28512000  barle^^-^'>J^.=^^5. 


I 


■^A 


i\ 


How  often  will  the  wheel  of  a  coach,  >hat 
ference,  turn  in  100  miles  ? 


e2 


Am.  b\j:-2  :  1/  :  i  i.er  ^--'^f,^., 
Jifis.  £111  :  3  :  '/.;  ^^^ 


r^ 


P^^^m^miSStiS^mi. 


Ifow  many  barley 
rmference  of  \,hicli  is 


REDUCTIOIV. 

* 

•corns  will   reach  round   the  world, 
360  degrees,  each  degree  69  miles 
Ans.  4755801600  barley-corni 

LAND  MEASURE. 


th 
and 


A 


63.  In  27  acres,  how  many  roods  and  perches? 

Ans.  108  roods,  4320  perches, 

64.  In  4320  perches,  how  many  acres  ?  Ans.  27. 

66.  A  person  having  a  piece  of  ground,  containing  37  acres.  1 
pole,  has  a  mind  to  dispose  of  15  acres  to  A.  I  desire  to  know 
how  many  perches  he  will  have  left  ? 

[.  ^  Ans.  3521. 

'  66.  There  are  four  fields  to  be  divided  into  shares  of  75  perches 

f  each ;  the  fii-st  field  containing  5  acres ;  the  second,  4  acres,  2 
poles ;  the  third,  7  acres,  3  roods ;  and  the  fourth,  2  acres,  1  rood, 
I  desire  to  know  how  many  shares  are  contained  therein  ? 

|^  •  Ans.  40  shares,  42  perches  rem, 

f  WINE  MEASURE. 

}  ' 

67.  Bouglit  5  tuns  of  port  wine,  how  many  gallons  and  pints? 
i  ^  Ans.  1260  gallons,  10080  pints. 

68.  In  10080  pints,  how  many  tuns  ?      '  Ans.  5  tuns. 
\    69.  In  5896  gallons  of  Canary,  how  many  pipes  and  hogs- 
heads, and  of  each  an  equal  number? 

-.   ^  Ans.  31  of  each,  37  gallons  over. 

70.  A  gentleman  ordered  his  butler  to  bottle  oflf  f  of  a  pipe 
of  French  wine  into  quarts,  and  the  rest  into  pints.  I  desire  to 
know  how  many  dozen  of  each  he  had  ? 

Ans.  28  dozen  of  each. 

ALE  AND  BEER  MEASURE 

71.  In  46  barrels  df  beer,  how  many  pints. 

Ans.  1.3248.     / 

L^    lb  ,  barrels  of  ale,  how  many  gallons  and  quarts? 

*        r    f,    .  -^***-  320  gals.  1280  qta.    / 

42.  I^»-»^  '  2  hogslioads  of  ale,  how  many  barrels"?  .  ' 


» 


common 


-j^f  ale,  how  many  hog-sheads  ? 


Ans 


xin^f 


%^parcel3  of  u 


Afuu.., 


,■#■ 


s. 

mi 


\ 


SINGLE   BULE    OF   THREE    DIRECT. 


^ 


15.  If  a  genflfeman's  income  is  £500  a  year,  and  he  spends  19^.  4d.  per 
day,  how  much  does  he  lay  by  at  the  year's  end  ?        \dtis.  £147  :  3  :  4. 

16.  If  I  buy  14  yards  of  cloth  for  10  guineas,  how  many  Flemish  ella 
can  I  buv  for  £283  :  17  :  6  at  the  same  rate  ?  ...j^^Jj^^^-: 

Ans.  a|KPit»W?>  2  qrs. 
f  17.  If  504  Flemish  ells,  2  quarters,  cost  £283  :  17  :  %mfc^at  rate  did 

I  pay  for  14  yards  .' 

Ans.  IDs.  lOd. 
18.  Gave  £1  :  1  :  8  for  3  lb.  of  coffee,  what  must  be  given  for  29  lb.  4  oz.  ? 

Ans.  £10  :  1 1  :  3. 
W.  If  one  English  ell  2  qrs.  cost  43.  7d.  what  will  39i  yards  cost  at  th« 

•ame  rate .' 

Ans.  £5:3:  54,  5  rem. 

20.  If  one  ounce  of  gold  is  worth  £5:4:2,  what  is  the  worth  of  one 
grain  .'  -Ans.  2h\.  20  rem. 

21.  If  14  yards  of  broad  cloth  cost  £9  :  12,  what  is  the  purchase  of  75 
yards  ?  '  -^ws.  51  :  8  :  G|,  G  rem. 

22.  If  27  yards  of  Holland  cost  £5  :  12  :  6,  how  many  ells  English  can 
I  buy  for  £100  ?  -/ins.  384. 

23.  If  1  cwt.  cost  £12  :  12  :  6,  what  must  I  give  for  14  cwt  1  qr.  19  lb. 

Ans,  £182  :  0:  lU,  8  rem. 

24.  Bought  7  yards  of  cloth  for  1 7s.  8d.  what  must  be  given  for  5  pieces, 
each  containing  27 i  yards. 

Ans.  £17  :  7  :  04,  2  rem. 

25.  If  7  oz.  11  dwts.  of  gold  bo  worth  £35,  whut  is  the  value  of  14  lb. 
0  oz.  12  dwt.  10  gr.  at  the  same  rate  ? 

Ans.  £823  :  9  :  3|,  552  rem. 

26.  A  draper  bought  420  yards  of  broad  cloth,  at  the  rate  of  i4s.  lO^d 
per  ell  English,  how  much  did  he  pay  for  the  whole  ? 

^  ^  •  jfr«.».  250  :  5. 

27.  A  gentleman  bftught  a  wedge  of  gold,  which  weighed  14lb..3oz 
8  dwts.  for  the  sum  of  £514  :  4,  at  what  rate  did  he  pay  fur  it  per  oz? 

Ans  £3. 

28.  A  grocer  bought  4  hogsheads  of  sugar,  «ach  weighing  nt  at  0  cwt.  2 
qrs.  14  lb.  which  cost  him  £2  :  8  :  G  ptr  cwt. ;  what  is  the  value  of  the  4 

hogsheads  ?  „   .  . 

^  '  Ans.  £04  :  5  :  3. 

29.  A  draper  bought  8  packs  of  clotli,  each  containing  4  parcels,  euch 
parcel  10  pieces,  and  each  f)iece  26  yards,  and  gave  after  the  rote  of  £4  % 
16  for  6  vards  ;  I  desire  to  linow  what  tlie  8  packs  stood  him  to  ? 

■^  Ans.  £jG56. 

30.  If  21  lb  of  raisins  cost  Gs.  Gd.  what  will  IS  frails  CDst,  encb  weigh- 
ing neat  3  qrs.  1 S  lb.  ?  ^  ^;- 

*^  ,        ..  Ans.  £24  :  \fi%. 

>  9J'/  JM  oz.  of  stiver  be  worth  5.3.  what  is  the  price  of  14  irtgot^s  eachS 

weighing  7  1b,  5  oz.  10, dwts.  <^ 

''      *        "  .  Ans.  £:jiy  :  5, 

a-_,^.       VTU^tL    i3    CttCpti'--    '•'     "    |-"--< 5 D     -    --■--     -     -•-      ^  \-^^ 

Old.  pKr  titwie? 


%.  Boa.^i!t  50  cwt.  2  qrs.  24  lb.  of  tobacco 
il^ioa  Uconie  to  i 


\ 


yimin  -i^^ifr   '  ' 


BULE    OF   THREE    INVERSE. 


34.  Bought  l7l  tons  of  lead,  at  £14  per  ton;  paid  carriage 
and  other  incident  charges,  £4  :  10.  I  require  the  value  of  the 
lead,  and  what  it  stands  me  in  per  lb.  ?  ,- . 

'  Ans.  £2398  :  10  value ;  H5ilk32  rem.  per  lb. 

35.  If  a  pair  of  stockings  cost  10  groats,  how  many  dozen  may 
I  buy  for  £43  :  5  ? 

Ans.  21  dozen,  7^  pair. 

36.  Bought  27  dozen  6  lb.  of  candles,  after  the  rate  of  17d. 
per  3  lb.  what  did  they  cost  me  ? 

Ans,  £7  :  15  :  4^,  1  rem. 
87.  If  an  ounce  of  fine,  gold  is  sold  for  £3  :  10,  what  come  7 
ingots  to,  each  weighing  3  lb.  7  oz.  14  dwts.  21  gr.,  at  the  same 


pnce 


Ans.  £1071 :  14  :  5^. 


38.  If  my  horse  stands  me  in  9^d.  per  day  keeping,  what  will 
be  the  charge  of  1 1  horses  for  the  year  f 

Ans.  £158  :  18  :  6^. 

39.  A  factor  bought  86  pieces  of  stuff,  which  cost  him  £517  : 
19  :  4,  at  4s.  lOd.  per  yard ;  I  demand  how  many  yards  ther« 
were,  and  how  many  ells  English  in  a  piece  t 

•      Ans,  2143^  yards,  56  rem.  and  19  ells,  4  quartei-s, 
2  nails,  64  rem.  in  a  piece. 

40.  A  gentleman  hath  an  annuity  of  £896  :  17  per  annum. 

I  deoire  to  know  how  much  he  may  spend  daily,  that  at  the  year's  ^^ 
end  he  may  lay  up  200^ guineas,  and  give  to  the  poor  quarterly 
40  moidores?  Ans.  £1  :  14  :  8,  44  rem. 


THE  RULE  OF  THREE  INVERSE. 


Inverse  Proportion  is,  when  more  requires  less,  and  less  re- 
quires more.  More  requii-es  less,  is  when  the  third  term  is  great- 
^er  than  the  first,  and  requires  the  fourth  term  to  be  less  than  the 
^cond.  And  less  requires  more,  is  when  the  third  term  is  le^ 
than  the  first,  and  requires  the  fourth  term  to  be  greater  than 
second. 

e  first  and  second  terms 


¥y 


togeth 


\o,  product  by  the  third,  the  quotient  will  bear  such  propof- 
M  second  as  the  first  does  to  the  third. 


(- 


RX7LE    OF  THREE    INVERSE. 


67 


EXAMPLES. 


r. 


it-      •  f 


1.  If  8  men  can  do  a  piece  of  work  in  12  days,  how  many 
days  can  IG  men  perform  the  same  in  ?  Ans.  C  days. 

8  .  12  .  .  16  .  6 
8 


16)90(6  days. 

2.  If  54  men  can  build  a  house  in  90  days,  how  many  can  do 
the  same  in  50  days  ? 

Ans.  974  men. 

3.  If,  when  a  peck  of  wheat  is  sold  for  2s.,  the  p«?nny  loaf 
weighs  8  oz.,  how  much  must  it  weigh  when  the  peck  is  worth 

but  Is.  Gd.  ?. 

Ans.  10|  oz. 

4.  How  many  pieces  of  money,  of  20s.  value,  are  equal  to 
240  pieces  of  12s.  each?te  Ans.  144. 

6.  How  many  yards,  oi  three  quarters  wide,  are  equal  in  .mea- 
iure  to  30  yards,  of  5  quartei*s  wide  ?  Ans,  60. 

6.  If  I  lend  my  friend  £200  for  12  months,  how  long  ought 
he  to  lend  me  £160,  to  requite  my  kindness? 

Ans.  16  months^ 
1.  If*  for  24s.  I  have    1200  lb.   carried  36  miles,  how  many 
pounds  can  I  have  carried  24  miles  for  the  same  money  ? 

Ans.  1800  lb. 

8.  If  108  workmen  finish  a  piece  of  work  in  12  days,  how 
many  arc  sufficient  to  finish  it  in  3  days  I 

Ans.  432. 

9.  An  army  besieging  a  town,  in  which  were  1000  soldiers, 
with  provisions  for  3  months,  how  many  soldiers  departed,  when 
the  provisions  lasted  them  6  months  ? 

Ans.  500. 

10.  If  £20  worth  of  wine  is  sufficient  to  serve  an  ordinary  of 
100  men,  when  the  tun  is  sold  for  £30,  how  many  will  £20 
wortljr  suffice,  when  the  tun  is  sold  but  for  £24  ? 

Ans.  125.    Jf' 

ii.il  Conner  makes  a  journey  m  i;4:  uuya,  wiji;ij   uio 

but  12  houi-s  long,  how  many  days  will  he  be  going  tli 
journey,  when  the  day  is  16  hours  lon^? 

Ans,  Ij 


' %if?f^-.ijU^f''^f\    ■  ■ 


69 


DOUBLE    RULE    OE    THREE. 


12.  How  much  plush  is  sufficient  for  a  cloak,  which  has  in  it 

4  yards,  of  1  quarters  wide,  of  stuff,  for  the  lining,  the  plush  being 

but  3  quarters  wide? 

Ans.  9^  yards. 

13.  If  14  pioneers  make  a  trench  in  18  days,  how  many  days 
will  34  men  take  to  do  the  same  ? 

Ans.  1  days,  4  hours,  56  min.  y\,  at  12  hours  for  a  day. 

14.  Borrowed  of  my  friend  £64  for  8  months,  and  he  had  oc- 
casion another  time  to  borrow  of  me  for  12  months,  how  much 
must  I  lend  him  to  requite  his  former  kindness  to  me  ? 

Ans.  £42  :  13  :  4. 

15.  A  regiment  of  soldiers,  consisting  of  1000  men,  are  to  hav* 
new  coats,  each  coat  to  contain  2^  yards  of  cloth,  5  quarters  wide, 
and  to  be  lined  with  shalloon  of  3  quarters  wide ;  I  demand  how 
many  yards  of  shalloon  will  line  them  ? 

Ans.  4166  yards,  2  qrs.  2  nails,  2  rem. 


THE  DOUBLE  RULE  OF  THREE, 


Is  so  called  because  it  is  composed  of  5  numbers  given  to  find  a 
6th,  which,  if  the  proportion  is  direct,  must  bear  such  a  proportion 
to  the  4th  and  5th,  as  the  third  bears  to  the  1st  and  2d.  Btit  if  in- 
verse, the  6th  number  must  bear  such  proportion  to  the  4th  and 
6th,  as  the  1st  bears  to  the  2d  and  3d.  The  three  first  terms  are 
a  supposition ;  the  two  last,  a  demand. 

Rule  1.  Let  the  principal  cause  of  loss  or  gain,  interest  or 
decrease,  action  or  passion,  be  put  in  the  first  place. 

2.  Let  that  which  betokeneth  time,  distance  of  place,  and  the 
like,  be  in  the  second  place,  and  tiie  remaining  one  in  tlie  third. 

3.  Place  the  other  two  terms  under  their  like  in  the  su}>posi« 
tion. 

4.  If  tlie  blank  falls  under  the  third  term,  multiply  the  first  and 
second  terms  for  a  divisor,  and  the  other  three  for  a  dividend. 
But, 

iail3     UHUCT     OtltJ     Hint     or     OCUVilUb     Ut 


u. 


11    Liro 


1-1 i_ 

UUUIIv. 


]yhxs  third  and  fourth  terms  for  a  divisor,  and  the  other  three  for 


jy^S^ivideiid,  and  the  quotient  will  be  tlie 
HLIt'^oof.  By  two  single  rules  of  three. 


answer. 


^.  *»iA-j(    -».-.«•»  *■- 


M,.. 


L;f  *'ii 


/ 


II    iili  I  I    ;)MB|ll>ili 


DOUBLE    RULE    OP    THREE. 


^jnSfcKL^ 


b^ 


EXAMPLES. 

^J'  U-  •  "^  I'^'^L^  u*  ^°  ^"^^^^^  °^  °^*«  i»  16  days,  how  many  bushels  will 
be  sufficient  lor  20  horses  for  24  days  ?  /  '»  «»" 


By  two  single  rules, 
hor.     bu.      hor.     bu. 

1.  As  14  .  50   ..  20  .  80 

days     bu.     days.     bu. 

2.  As  10  .  80  . .  24  .  120 


or  in  one  stating,  worked  thus : 
hor. 'days    bu. 
14  .   Id  .  50    50X20X24 

20  .  24  .  ^    _=120 

14X10 


#h?:  ^l  ^.""'"  i*14  days  can  mow  112  acres  of  grass,  how  many  men  must 
there  be  to  mow  2000  acres  in  10  days  ?  ' 

acres,   days,    acres,     days.    ;     men.  days,  acres. 
.1.  As  112  .   14  ..  2000  .  250      r         8    .  14    .  112.8X14X2000 


days. 
As  250 


rnen.     davs. 
8  ..     10 


men. 
200 


10   .  2000  112X10 


-=200 


3.  If^lOO  in  12  months  gain  £6  interest,  how  much  will  £75  eain  in 
-^  '"''"^^s-  ^m.  £3:7:6. 

much  inthf  hil'''^'''''%^\*  ^  ^"'-'^^  ''"'"""S^  «^  3  '^^•*-  150  miles,  how 
much  ought  he  to  receive  for  the  carnage  of  7  cwt.  3  qrs.  14  lb.  for  50  miles  ? 

r    ,,  .  •  -^ns-  £1:10:  9. 

tP.^;nf  whS"^^?no^/''^^'r''  ^^nsisting  of  136  men,  consume  351  quar- 

rnn.nmrr„  4";  ^^^^y^'  ^°^  "^^^^  quarters  of  wheat  will  11232  soldiers 
consume  m  56  days  ? 

%  -^ns.  15031  qrs.  804  rem. 

6.  II  40  acres  of  grass  be  mowed  by  8  men  in  7  days,  how  many  acres 
can  be  mowed  by  24  men  in  28  days  ?  ,/ins  480 

for'^oi  d«v,''  wnll  r^  ^  ""'"  ^°'  ^  ^^y^'  ™^^'  ^°^  "^"^h  vvi)rpay'32  men 
lor  -4  aa}s  woilc  f  ^^^^   ^33  .  ^ 

8    If  £100  in  12  months  gain  £0  interest,  what  principal  will  gain  £3  : 
7  :  0  in  9  months  ?  JJnl  £15. 

■   '^  /ioV^^''^''"*'  consisting  of  939  soldiers,  consume  351  qrs.  of  wheat 
m  a  108  days,  how  many  soldiers  will  consume  1404  qrs.  in  56  days  ? 

.ins   fl2G8. 
Ul  If  a  family  consisting  of  7  persons,  drink  out  2  kilderkins  of  beer  in 
12  days,  how  many  kilderkins  will  another  family  of  14  persons  drink  out 
'"  ^  "*^^  •  ^ns.  2  kil.  12  gal 


n 


11.  If  the  carriage  of  60  cwt.  20  miles,  cost  £14  :  10,  what  weii?ht  can  I   i 

have  carried  30  miles  for  £5:8:  9,  at  the  same  rate  of  carriage  f  f 

^      .  ^dns.  15  cwt.     / 

J^'Jnr?  ^'°T^  *•'*'  ^  ^"^^^^'^  °^°^^^  '"  16  ^ays,  how  many  horses  will  e^S 
up  JOOO  quarters  in  24  days  ?  .  'M 

Ans.  4Qr' 
13.  If  £100  in  12  months  gain  £7  interest,  what  is  the  interest  of^ 
for  6  years  ?  mt'- 

_e'^:'^'^S:~^ZT-   ...  ^»M*  ^839  :  16  :  4ifA 


„„«•— «r!rv 


60 


PBACTICB. 


^f  9  tons  6  miles,  wbat  must 
U.  If  I  pay  lOs.  f- ^^^C'^V  vvlTxnUesS  . 

I  pay  for  the  carriage  of  12  tons,  n       ^         ^^  ^9  .  2  -.  0^ 


\ 


PRACTICE 
ed  in  trade  and  business.  rf^^ed  by  taking  alW"?*'  «'. 

Of  a  Hundred. 

qrs.    lb. 
2  or  56  is  ^ 
1  or  28... l 
14. ..i 

Of  a  Quarter. 

14  lb I 

7 i 


4  ■ 


4 


3i 


the  answer.  ,. 

/i\  i;ai^^'704lb.  att  1                     ^1  ^♦^  6547  at  S 

Vv       12)1*'-"'  I  Faot,  £lb_^-n_    '_ . 

>\ -            \- ~„    ,,  (n  4573  at  i 


^ 


1€>; 


? 


;t.£5:18:10 


tban  a  sWlUng,  take  the  all 


"by  20,  as  before. 


O 


'»*'*%- 


IJ"^' 


ust 


cem- 

)t,  or 
ided; 


ndred. 
6i9  i 

Quarter. 

»  •  •  •  •  2 

i 

•  •  •  •  •f 
i 


!  by  tho 
,  will  bo 


TV  , 

%-•  .,  ■ 

to  tbe  all 
jetber,  and 


(»)  is  tV  7547  at  Id. 

210)6218  :  11 

Facit,  £31  :  8  :  11. 

(«)lis_U375latUd 

i  is  i  312  :  V 

78  :  H 


2i0)39l0  :  8| 

Facit,  £19  :  10  :  Si 

(")  ,5432r/at  1-H- 
Facit,  £339  :  10  :  7|. 

(*)  6254  at  Ud. 
Facit,  £45  :  12  :  0^ 

C*)  2351  at  2d. 
Facit,  £19  :  11  :  10. 

(«)  7210  at  2 id. 
Facit,  £67:11  :  10^. 

n  2710  at2^d. 
Facit,  £28  :  4  :  7. 


PRACTICE. 

(")  3257  at  4d. 
Facit,  £54  :  6  :  8. 

n  2056  at  4id. 
Facit,  £36  :  8  :  2.  =* 

("•)  3752  at  4id. 
Facit,  £70  :  7  :  0. 

(")  2107  at  4td. 
Facit,  £41: 14:  O-i 


(")3210at5d. 
Facit,  £66  :  17  :  6. 


n  2715  at5|d. 
Facit,  £59  :  7  : 


('*)  3120  at  5id. 
Facit,  £71  :  10  :  0. 

(")  7521  at  6fd. 
Facit,  £180  :  3  :  9|. 

{^')  3271  at  6d.      T 
Facit,  £81  :  15  : '6. 


C)    3250  at  2H 
Facit,  £37  :  4  :  9^. 

0  2715  at  3d. 
Facit,  £33  :  18  :  9. 

'{>')  7062  at  aid. 
Facit,  £95  :  12  :  7f 

{'')  2147  at  3|d. 
Facit,  £31:6:  2|. 

n  7000  at  3H 
Facit,  £109  :  7  :  6. 


n  7914  at  6id. 
Facit,  £206  :  1  :  lOf 

(")  3250  at  6^d. 
Facit,  £88  :  0  :  5. 

(")  2708  at  6H. 
Facit,  £76  :  3  :  3. 

{'")  3271  at  7d. 
Faeit,  £95  :  8  :  1. 

{'°)  3254  at  lid. 
Facit,  £98  :5:  Hi 

(")  2701  at  7id. 
Facit,  £84  :  8  :  H. 


61 

(")  3714  at  7|d. 
Facit,  £ll9:18:7f 

(")  2710' at  8d. 
Facit,  £90  :  6  :  8. 

C")  3514  at  8id. 
Facit.  £120: 15  :10J. 

(")  2759  at  8^d. 
Facit,  £97  :  14  :  3,f 

(''*)  9872  at  8^d. 
Facit,  £369  :  18  :  4. 

('')  5272  at  9d. 

Facit,  £197  :  14  :  0. 

/ ^^__ 

'("*)  6325  at  9id. 
Facit,  £243  :  15  :  6^. 

{^')  7924  at  9^d. 
Facit,  £313  :  13  :  2. 

('")  2150at  9|d. 
Facit,  £87  :  6  :  lOf 

(")  6325  at  lOd. 
Facit,  £263:10:10. 

n  5724  at  lO^d. 
Facit,  £244  :  9  :  3. 

n  6827  at  lOid. 
Facit,  £270  :  4  :  S^. 

•(")  3254  at  lO^d. 
Facit,  £142  :  7  :  3. 

{*')  7291  at  10^ 
Facit,  £326:11:6' 


1 


0. 

y 


.'»**;  ^left'V 


.\ 


(")  7254  at  lUd. 
Facit,  £340  :  0  :  7i 


PRACTICE. 

(**)  3754  at  ll^d. 
Facit,  £179  :  17  :  7. 


(")  7972  at  ll|d. 
Facit,  £390  :  5:11. 

Rule  3.  When  the  price  is  more  than  one  «^^ili«S' ^"^  .|f;^ 
than  two,  take  the  part  or  parts,  with  so  much  of  the  given 
priTe  n  more  than  a  shilling,  which  add  to  the  given  quantity, 
and  divide  by  20,  it  will  give  the  answer. 


('UxV2106atl2id. 
^^     *        43  :  lOi 


210)21419  :  10^ 

Facit,  £107  :  9  :  10^. 

{")  3215  at  Is.  lid. 
Facit,  £177:9  :10i 


Oi2i37l5atl2H 
154  :  9^ 


(•)  2790  at  Is.  l^d. 
Facit,  £15G  :  18  :  9. 

(')  7904  at  Is.  Ifd. 
Facit,  £452  :  16  :  8. 

(«)  3750  at  Is.  2d. 
Facit,  £218  :  15  :  0. 

(»)  3291  at  Is.  2id. 
Facit,  £195  :  8  :  Of. 


210)38619  :  9^. 

Facit,  £193  :  9  :  9i 

(")  3254  at  Is.  3|d. 
Facit,£213:10:10i 

('«)  2915  at  Is.  4d. 
Facit,  £194:6  :  8. 


(=>)  2712  at  125d. 
Facit,  £144  :  1  :  6. 


(*)  2107  at  Is.  Id. 
Facit,  £114  :  2  :  7. 


(")  9254  at  Is.  2|d. 
Facit,  £559  :  1  :  11. 

(")  7250  at  Is.  2fd. 
Facit,  £445:ll:5i 

(")  7591  at  Is.  3d. 
Facit,  £474  :  8  :  9. 


(")  G325  at  Is.  3id. 

•^^ .    fi.      O^rvi.io.nl 

racii,  ^^ivi  .  io  .  u^ 

'(")  5271  at  Is.  3^d. 
^Kacit,  £340:8  :4^d. 


(")  3270  at  Is.  Hd. 
Facit,  £221  :  8  :  li 

(»')  7059  at  Is.  4^d. 
Facit,  £485  :  6  :  li 

('")  2750  at  Is.  4fd. 
Facit,  £191:18:6|. 

(»°)  3725  at  Is.  5d. 
Facit,  £2G3  :  17  :  1. 

{^')  7250  at  Is.  5id. 
Facit,  £521 : 1  :  10^ 

("^)  2597  at  Is.  5^d. 
Facit,  £189  :  7  :  3i 

(")  7210  at  Is.  5fd. 

n  7524  at  Is.  6d. 
Facit,  £564  :  6  :  0. 


(")  7103  at  Is.  6id. 
Facit,  £540  :  2  :  5|. 

(")  3254  at  Is.  G^d. 
Facit,  £250  :  1^':  7. 

(")  7925  at  Is.  6|d. 
Facit,  £619  :  2  :  "' 


(")  9271  at  Is.  7d. 
Facit,  £733  :  19  :  1. 

(")  7210  at  Is.  7id. 
Facit,  £578  :  6  :  0^. 

n  2310  at  Is.  7^. 
Facit,  ^187  :  13  :  9. 

(")  2504  at  Is.  7^. 
Facit,  £206  :  1  :  2. 

C^)  7152  at  Is.  8d. 
Facit,  £590  :  0  :  0. 

{^^)  2905  at  Is.  8id. 
Facit,  £245  :  2  :  2\. 

(3*)  7104  at  Is.  8H 
Facit,  £606  :  16  :  0. 


PRACTICE. 


k^ 


(")  1004  at  Is.  8^d. 
Facit,  £86  :  16  :  1. 

(")  2104  at  Is.  9d. 
Facit,  £184  :  2  :  0. 

(")  2571  at  Is.  9icl. 
Facit,  £227  :  12  :  9i 

n  2104  at  Is.  Old. 
Facit,  £188  :  9  :  8. 

♦     n  7506  at  Is.  9^d. 
Facit,  £680  :  4  :  7^ 


n  1071  at  Is.  lOd. 
Facit,  £98  :  3  :  6. 

(")  5200  at  Is.  lO^d 
Facit,  £482  :  1  :  8. 


(")  2117  at  Is.  lO^d. 
Facit,  £198  :  9  :  4^ 

(")  1007  at  Is.  lOi 
Facit,  £95  :  9  :  1^. 

(**)  5000  at  Is.  lid. 
Facit,  £479  :  3  :  4. 


(")  2105atls.  ll^d. 
Facit,  £203  :  18  :  6^. 

\")  1006atl8.  ll^d. 
Facit,  £98  :  10  :  1. 

(")  2705atls.  ll|d. 
Facit,  £267  r^-a^-ai 

(")  5000  at  Is.  11 -^d.    J 
Facit,  £48P  :  11  :  8. 

n  4000atls.  llH 
Facit,  £395  :  16  :  8. 


RuLE  4.  When  the  price  consists  of  any  even  number^ of 
shillings  under  20,  multiply  the  given  quantity  by  half,  the  price, 
doubling  the  first  figure  of  the  product  for  shillings,  and  the  rest 
of  the  product  will  be  pounds. 


(»)  2750  at  2s. 
Facit,  £275  :  0  :  0. 

(")  3254  at  4s. 
Facit,  £650  :  16  :  0. 

(=■)  2710  at  6s. 
Facit,  £813  :  0  :  0. 

(*)  1572  at  8s. 
Facit,  £628  :  16  :  0. 


(')  2102  at  10s. 
Facit,  £1051  :  0  :  0. 

(«)  2101  at  12s. 
Facit,  £1260  :  12  :  0; 

{')  5271  at  14s. 
Facit,  £3689  :  14  :  0. 


0  3123  at  163.  ..    „ 

Facit,  £2498  :  8  :  0.  |  10s. 


(»)  1075  at  16s. 
Facit,  £860  :  0  :  0. 

(>»)  1621  at  18s. 
Facit,  £1458:18:0. 

Note.  When  the 
price  is  10s.  take  half 
of  the  quantity,  and 
if  any  remains,  it  ii 


■    Rule  5.    When  the  price   consists  of  odd  shillings,  multiply 
the  given  quantity  by  the  price,  and  divide  by  20,  the  quotient  - 
will  be  the  answer. 


(*)  2703  at  Is. 
Facit,  £135  :  3  :  0. 


(')      3270  at  3s.    '", 


210)98110 

Facit,  £490  :  10  :  0. 
i2 


0  3271  at  5s. 
Facit,  £817  :  15  :  0. 

J" 


Ki^mr    '^t  ■ 


'•^J«**^lM*'^ 


['-  iji/iiir 


G4 

(«)  2715  cat  7s. 
Facit,  £950  :  5  :  0. 


(')  3214  at  9s. 
Facit,  £1446  :  6  :  0. 


(•)  2710  at  lis. 
Facit,  £1490  :  10  :  0. 


rRACTICB. 

n  3179  at  13s. 
Facit,  £2066  :  7  :  0. 

C)  2150  at  15s. 
Facit,  £1612  :  10  :  0, 


(")  2150  at  199. 
Facit,  £2042  :  10  :  0. 

{'')  7157  at  19s. 
Facit,  £6799  -.3:0. 


(»)  3142  at  17s. 
c,t  *i4yu-..u.v.  Facit,  £2670 :  14 : 0.  .      ,     ,        . 

tol    When  the  price  is  5s.  divide  the  quantity  by  4,  and 
if  any  remain,  it  is  5s.  . 

T>        p    Whon  the  m-ice  is  shillings  and-  pence,  and  they  the 
Rule  6.  ^^^^  "'^  P'^ide  by  the  aliquot  part,  and  it  will 
aliquot  P'^'-t  o^  ^  Pf""^' ^'V,,t /thc^  aliquot  part, 

r  '^t^lHL  QuS  by      0  sSlh^        and  takeSxvrts  for 
then  inultq)ly  the  quanuiy   uy     ,.  . ,    ,     oo 
thd^rest,  add  thei*  together,  and  dn  ide  by  ^0. 

'  C)  7514  at  4s.  7d. 

Facit,  £1721  :  19  :  2. 


(^)  2710  at  6s.  8d. 
Facit,  £903  :  6  :  8. 

(')  3150  at  3s.  4d. 
Facit,  £525  :  0  :  0. 


(^)  2715  at  2s.  6d. 
Facit  £339  :  7  :  6. 


(*)  7150  at  Is.  8d. 
Pacit,  £595  :  16  :  8. 


[")  3215  at  Is.  4d. 
Facit,  £214  :  6  :  8. 

C)  7211  at  Is.  3d. 
Facit,  £450  :  13  :  9. 

[')  2710  at  33.  2d. 
3 

8130 
451  :  8 


85811  :  8 


Facit,  £429  :  1  :  8. 


(»)  2517  at  5s.  3d. 
Facit,  £660  :  14  :  3. 

(»")  2547  at  78.  3|d. 
Facit,  £928: 11: 10  J. 

{'')  3271  at  5s.  9^d. 
Facit,  £943:  16  :  4i    . 

('")  2103  at  15s.  44d. 
Facit,£1616:13:7i 

('")  7152  atl7s,  6H 
Facit,  £6280  :  7  :  0. 

('*)  2510  at  14:  7^d. 
Facit,  £1832  :J  6 :5i. 

('")  3715  at  9s.  4^d. 
Facit,  £1741:  8  :  1^. 

('«)  2572  at  13  :  7^d. 
Facit,  £1752  :  3  :  6. 


(")  7251  at  14s.  8\d. 
Facit,£5324:19:0|. 


PRACTICE. 


65 


C. 


(")  3210  at  15s.  7|d. 
Facit,  £2511  .3.1^. 


l(")2YlO  at  19s.  2icL 
Facit,  £2602. 14.  7. 


RuLK  1:  Ut,  When  the  price  is  pounds  and  shillings,  multiply 
the  quantity  by  the  pounds,  and  proceed  with  the  shillings,  if 
they  are  even,  as  the  fourth  rule ;  if  odd,  take  the  aliquot  parts, 
add  them  together,  the  sum  will  be  the  answer. 

2dly,  When  pounds,  shillings,  and  pence,  and  the  shillings  and 
pence  the  aliquot  parts  of  a  pound,  multiply  the  quantity  by  the 
pounds,  and  take  parts  for  the  rest. 

3dly,  When  the  price  is  pounds,  shillings,  pence,  and  far- 
things, and  the  shillings  and  pence  are  not  the  aliquot  parts  of  a 
pound  reduce  the  pounds  and  shillings  into  shillings,  multiply 
the  quantity  by  the  shillings,  take  parts  for  the  rest,  add  them 
together,  and  divide  by  20. 

Note.  When  the  given  quantity  consists  of  no  more  than 
three  figures,  proceed  as  in  Compound  Multiplication. 


s.  d. 
2:6 


6 


1 

6 


{')  7215  at  £7.  4.0. 
Y 


1 

5 


50505 
1443 

£51948 


ft,- 


6 


H 


i 


0  2104  at  £5.3.0 
5 


(■*)  27lOat£2.3.7i. 
43 


210 


10520 
263 
52.12 

£10835.12 


(3\  Oin'7  of    -P9,     R  .0. 

Facit,  £5056.16.0. 

(')  7156  at  £5  .6.0. 
Facit,  £37926. 16.0. 

F3 


V 


116530 
1355 
338.9 

1182213.9 


Facit,  £5911  .3.9. 

('')3215at£l  .17.0. 
Facit,  £5947.  15.0. 


(')  2107  at £1.1 3.0. 
Facit,  £3476.11  .  0. 

(«^  3215  at  £4.6.8. 
Facit,  £1393 1.1 3.  4. 


(»)  2154  at  £7.1  .3^ 
Facit.  £15212. ;5>'" 


,K.^ 


««<«»#'*'** 


<      f 


66 


PRACTICE. 


('»)  2701  at  £2.  3. 4. 
Facit,  £5852  .3.4. 

(")27l5iit£l.l7.2i. 
Fncit,  £5051  .0.7^. 

('^)2157at£3.15.2i. 
Kiicit,£8l08.19.5i. 

('=)3210at£1.18.6i 
Facit,  £G189.5.7i 

('*)2157at£2.7.4i 
Facit,  £5109.  7.  loi 


("^)142at£l.l5.2i 
Facit,  £250  .  2  .  6i. 

("')95at£l5.14.7i. 
Facit,  £1494.  7.  4i 

(")37at£1.19.5i 
Facit,  £73  .  0  .  8$. 

n  2175  at  £2.15.4^. 
Facit,  £G022,0.7|.' 

('»)2150at£l7.l6.U. 
Facit,  £38283  .8.9. 


Rule  8.  When  the  price  and  quantity  given  are  of  several 
denominations,  multiply  the  pri  by  the  integers,  and  take  parca 
with  the  parts  of  the  integers  fo    .ne  rest.  ^ 

1.  At  £3  .  17  .  G  per  cwt.,  what  is  the  value  of  25  cwt.  2  qrs.  14 
lb.  of  tob^co  ? 


h 


lb. 
14 


£3.17.  6 

5X5=25. 


19.  7.  6 
6 


i 


96.17.  6 
1.18.  9 
9.  8i 


99.  5.1U 


y'^' 


o    At  £1  .  4  .  9  per  cwt,  what  comes  17  cwt.  1  qr.  17  lb.  of 
,  ^     .    2  Ans.  £21  .  10  .  0. 

S^'sold  85  cwt.  1  qr.  10  lb.  of  cheese,  at  ^l;.^^^^  p^^  cwt., 

what  does  it  come  to?  ,  ^f  •  ^}^^ '^  '  ^,^-  . 

4.  Hops  at  £4  .  5  ,  8  per  cwt.,  what  must  bo  g'v^n  for  72  cwt. 

"  ^"  At  £1  .  1  .  4  per  cwt.  what  is  the  value  of  27  c^vt.  2^  qrs. 


15  lb.  of  Malaga  raisins 


Ans.  £29  .  9  .  C^. 


6 


Bouo-ht  IS  cwt.  3  qrs.  12  lb.  of  currants,  at  £2     17  .  9  per 


cwt.*  what" did  I  give  for  the  whole? 


Ans.  £227  .  14. 


w 


SIJ 


Q9 


.2i 
6^. 

.4i 
.  5i 

8i 

5.4^. 

»    7-1.  . 

i6.1i 
8.9. 

ovcral 
parts 

rs.  14 


lb.  of 
)  .  8. 
cr  cwt., 
.  oi 
72  cwt. 
?  .  2. 

2  qra. 

.  9  per 
.14. 


1' 


TARE    AND   TRET  * 

J-  Sold  56  cwt.  1  nr    ni)      .  '  ^^ 

^hat  docs  it  come  to?^  *  '^  ^^'  '^  '^^S^^>  at  £2  :  15  :  0  the  cwt 

c^...,U  ;•"•  ^°  «^-'vt..  w,.at,-s  the  worth    f^r 

^«  ib.  of  do„b,„^;|,<!^4:VW.at  i3  tho  v«,„o  of  av'e.!!  2  ,^  \j 

'«  C'vt  1  <,r.  ,0  jb.  J  '*  •  8  the  cwt.,  what  did  I  gi,,  f„ 

»f  '"W tj;i -^  -..  the  va,„e  of  nl^ 3^  l^^, 

nfu--'---hee^,whatf;i^S;--;^ 

^«5.  i)l90:  0:4. 


.^■' 


TARE  AND  T/^et. 


«&       —  .Jxu  Pure  wcio-iif  «.u^„    „     „       --^'-^^t-cu  irom  f./i^  fY.«^„^ 

^en  all  aJIowan, 


.      i^ 


1 


T      I*" 


1     ^|j  -  are  deducted. 


ff''oss,  the  reRtaindci 


?s  neat. 


m«.j„»-.-^.^— .,.»WT*«r^-  • 


*.-^.«  \«0l^_  Ml,  'VIP 


"*'*1?R**^»«w»^»«*^ 


es 


TARE  AND  TRET. 


Note.  To  reduce  Pounds  into   Gallons,  multiply  by  2,  and 

^^1  ^In^7  frails  of  raisins,  each  weighing  5  cwt.  2  qrs.  5  lb.  gross, 
tare  at  23  lb.  per  frail,  how  much  neat  we^-hU  ^^^  ^  ^^  ^^  ^^ 

23  5.2.5  or,5.2.^5 

28)161(5  38.3.    ^=gross  ^  *  ^  *  ^2 

140- 1.1.  21=tare  ^ 

^    *  37  .  1  .  14=neat  37  .  1  .  14 


2    What  is  the  neat  weight  of  25  hogs^     .ds  of  tobacco,  weigh- 
ing gross  163  cwt.  2  qrs.  15  lb.,  tare  100  xo  per  hogshead? 
^  ^  Ans,  141  cwt.  1  qr.  7  lb. 

3.  In  16  bags  of  pepper,  each  85  lb.  4  oz.  gross,  tare  per  bag, 
3  lb.  5  oz.  how  many  pounds  neat  ?  ^»*«-  1^^  J^- 

Rule  2.  When   the  tare  is  at  so  much  in  the  whole  gross 
weig^,  subtract  the  given  tare  from  the  gross,  the  remamder  is 

"^4'  What  is  the  neat  weight  of  5  hogsheads  of  tobacco,  weigh- 
ing gr6ss  75  cwt.  1  qr.  14  lb.,  tare  in  the  whole  752  lb.  ? 
»  ^  An^.  68  cwt.  2  qrs.  18  lb. 

5.  In  75  barrels  of  figs,  each  2  qrs.  27  lb.  gross,  tare  in  the 
whole  597  lb.  how  much  neat  weight?  Ari^.  50  cwt.  1  qr. 

Rule  3.  When  the  tare  is  at  so  much  per  cwt.,  divide  the 
gross  weight  by  the  aliquot  parts  of  a  cwt.,  which  subtract  from 
the  gi'oss,  to  remainder  is  neat. 

Note.  7  lb.  is  i^,  8  lb.  is  ^V,  1^  lb-  «  i,  16  lb.  is  f 

6.  What.is  the  neat  weight  of  18  butts  of  currants,  each  8  cwt 
2  qrs.  5  lb.,  tare  at  14  lb.  per  cwt.?  \ 

^  8.2.5 

9X2=18 


76  .  3  .  17 


14=^  153  .  3  .    6 
19  .  0  .  25i 


.cwt.,  w 


134  .  2 


8^ 


^rg. 

0  per 
14. 


^    ,12. 
^  15 

\  lb 

"1 


and 


TARB    AND   TIJET. 


m 


1  In  25  barrels  of  figs,  each  2  cwt.  1  qr,  gross  tare  per  cwt 
16  lb.,  how  much  neat  weight?  Ans.  48  cwt.  0  qr.  24  lb. 

8  What  is  the  neat  weight"  of  9  hogsheads  of  nutmegs,  each 
weio-hing  gross  '8  cwt.  3  qrs.  14  lb.,  tare  16  lb.  per  cwt. 

°     *=  ^  Ans.  68  cwt.  1  qr.  24  lb. 

Rule  4  When  tret  is  allowed  with  tare,  divide  the  pounds 
suttle  by  26,  the  quotient  is  the  tret,  which  subtract  from  the  sut- 
tle,  the  remainder  is  neat. 

9.  In  1  butt  of  currants,  weighing  12  cwt.  2  qrs.  24  lb.  gross 
tare  14  lb.  per  cwt.,  tret  4  lb.  per  104  lb.,  how  many  pounds  neat  ? 

12  .  2  .  24 
4 


i 
9  per 

.14. 


60 
28 


14=1^  1424  gross. 
178  tare. 


26)1246  suttle. 
47  tret. 


1199  neat. 


10.  In  7  wt.  3  qrs.  27  lb.  gross,  tare  36  lb.,  tret  4  ib.  per  lO-* 
lb.,  how  many  pounds  neat?  ^^,.  826  lb. 

11.  In  162  cwt.  1  qr.  3  lb.  gi'oss,  tare  10  lb.  per  cwt.,  tret  4  lb. 
per  1041b.,  how  much  neat  weight? 

^  Ans.  133  cwt.  1  qr.  12  lb. 

Rule  6.  When  cloff  is  allowed,  multiply  the  cwts.  suttle  by 
2,  divide  the  product  by  3,  the  quotient  will  be  the  pounds  cloff, 
which  subtract  from  the  suttle,  the  remamder  will  be  neat.  . 

J.    1  o   i7tn.«f ;.  tL«  nnaf.  wmD'ht  of  3  hosfsheads  of  tobacco,  weigh 


itoV  15  cwt.  3  qrs.  20  lb.  gross 


I 


tare  7  lb.  per  cwt.,  tret  4  lb.  per 


\  lb.,  cloff  2  1b.  for  3  cwt.? 


I 


Ans,  14  cwt.  1  qr. 


3  lb. 


70 


INTEREST. 


zJ^  15  .  3  .  20    gross. 
3  .  27i  lare. 


26)14  .  3  .  20i  suttle 
3  .    8    tret. 


14  .  1  .  12i  suttle. 
9i  doff. 


14  .  1 .    3 

13.  In  7  hogsheads  of  tobacco,  each  weighing  gross  5  cvvt.  2  qrs.  7  lb., 
tare  S  lb.  per  cwt.,  tret  4  lb.  per  104  lb.,  cloff  2  lb.  per  3  cwt.,  how  much 
neat  weight  i  -^ns.  34  cwt.  2  qrs.  8  lb. 

SIMPLE   INTEREST, 

Is  the  Profit  allowed  in  lending  or  forbearance  of  any  sum  of  money  for  a 
determined  space  of  time. 

The  Principal  is  the  money  lent,  for  which  interest  is  to  be  received. 

The  rate  per  cent,  is  a  certain  sum  agreed  on  between  the  Borrower  and 
the  Lender,  to  be  paid  for  every  £100  for  the  use  of  the  principal  12  months. 

The  Amount  is  the  principal  and  interest  added  together. 

Interest  is  also  applied  to  Commission,  Brokage,  Purchasing  of  Stocks, 
and  Insurance,  and  are  calculated  by  the  same  rules. 

To  Jind  the  Interest  of  any  Sum  of  Monet/  for  a  Tear. 

Rule.  1  Multiply  the  Principal  by  the  Rate  per  cent.,  that  Product  divi« 
ded  by  100,  will  give  the  interest  required. 


<'M 


For  several  Years. 


2.  Mtt\tiply  the  interest  of  one  year  by  the  number  of  years  given  in  the 
qawtionS|nd  the  product  will  be  the  answer. 

§:  wrlittre  be  parts  of  a  year,  as  months,  weeks  and  days,  work  for  the 
montHI'lby  tMe  aliquot  parts  of  a  year,  and  for  the  weeks  and  days  by  the 
Rule  of  Three  Direct. 

'  V  J  EXAMPLES. 

1.  What  is  the  interest  of  £375  for  a  year,  at  5  per  cent,  per  annum  ? 

5 


15100    Ans.  £18  .  15  .  0. 


2  Whit  is  ike  interest  of  £268  for  1  year,  at  4  per  cent,  per  annum 

Ans.  £10  .  14  .  41 

3  Wha^u  the  interest  of  £945  .  10.  for  a  year,  at  4  per  cent,  per  annu 

*  T  Jim.  37  .  16  .  4| 


^^..4i 


,;apc-.. 


INTEREST. 


'* 


qrs.  7  lb., 
how  much 
lis.  8  lb. 


loney  for  a 

received, 
rrower  and 
12  months. 

of  Stocks, 


Year. 
oduct  divi- 


riven  in  the 

ork  for  the 

days  by  the 


r  annum  ? 


4.  What  is  the  interest  of  £547  .  15,  at  5  per  cent,  per  annum,  for  3 
years  .>  Ans.  £82  .3.3. 

5.  What  is  the  interest  of  £254^  17  .  6,  for  5  years,  at  4  per  cent,  pe? 
annum  .>  Ans.  £50  .  19  .  6. 

6.  What  is  the  interest  of  £556  .  13  .  4,  at  5  per  cent,  per  annum,  for 
6  years  ?  Ans.  £139  .  3  .  4. 

7.  My  correspondent  writes  me  word,  that  l)e  has  bought  goods  to  the 
amount  of  £754  .  16  on  my  account,  what  does  his  commission  come  to  at 
2i  per  cent.  ?  ,     Ans.  £18  .  17  .  4|. 

8.  If  I  allow  my  factor  3|  per  cent,  for  commission,  what  may  he  de- 


mand on  the  laying  out  £876  .  5  .  10  .' 


Ans.  £32  .  17  .  2i. 


9    At  llOi  per  cent.,  what  is  the  purchase  of  £2054  .  16.  South  Sea 
Stock  ?  Ans.  £2205  .8.4. 

10.  At  104g  per  cent.  South  Sea  annuities,  what  is  the  purchase  of  179TF  . 
14?  -    Ans.  £IS1(S  .  Q  .  m. 

11.  At  96|  per  cent.,  what  is  the  purchase  of  £577  .  19,  Bank  annuities  ? 

Ans.  £559  .  3  .  3|. 

12.  At  £124§  per  cent.,  what  is  the  purchase  of  £758  .  17  .  10,  India 
Stock  ?  £945  .  15  .  4i. 

BROKAGE, 

Is  an  allowance  to  brokers,  for  helping  merchants  or  factors  to  persons,  to 
buy  or  sell  them  goods.       ^ 

RuLK.     Divide  the  sum  given  by  100,  and  take  parts  from  the  quotient 
with  the  rate  per  cent. 

13.  If  I  employ  a  broker  to  sell  goods  for  me,  to  the  value  of  £2575  . 
17  .  6,  what  is  the  biokage  at  4s.  per  cent.  ? 

25175.17.6 

20  4s.=:}25.'l5.2 

Ans.  £5  .    3.04 


•Si#' 


r  annum 
.  14  .  41 
perannu 
.  16  .  4i 


15117 

12  ■ 

2110       •  ;- 

14.  When  a  broker  sells  goods  to  the  amount  of  £7105  .  5  .  10,  what 
may  he  demand  for  brokage,  if  he  is  allowed  5s.  6d.  per  cent.  ? 

Ans.  £19  .  10  .  9|. 

15.  If  a  broker  is  employed  to  buy  a  quantity  of  goods  to  the  value  of 
£975  .6.4,  what  is  the  brokage,  at  63.  6d.  per  cent.  ? 

wins.  £3  .  3  .  4i 

16.  What  is  the  interest  of  £547  .2.4,  for  5i  years,  at  4  per  cent,  per 
annum  .^  -•  Ana.  £120  .  7  ,  3i 

17=  What  is  the  interest  of  £257  ,5  =  1,  at  4  per  eent=s  for  a  vear  and 
three  quarters  ?  Ans.  £1$  .  6  .  li. 

18.  What  is  the  interest  of  £479  .  5  for  54  years,  at  5  per  cent,  per  an- 
num .'  Ans.  £125  .  16  .  0| 


73 


INTEREST. 


Itp 


19.  What  is  the  interest  of  £576  :  2  :  6  for  1^  years,  a.|  4|  per 

cent,  per  annum. 

Jns.  £18'7  :  19  :  2^. 

20.  What  is  the  interest  of  £279  :  13  :  8  at  5^  per  cent,  per 

annum,  for  3^  years  ? 

Ans.  £51:1  :  10. 

When  the  interest  is  required  for  any  nuiuhcr  of  Weeks. 

Rule.   As  52  weeks  are  to  the  Interest  of  the_  given  sura  for 
a  year,  so  are  the  weeks  given  for  the  interest  i-equired. 

21.  What  is  the  interest  of  £259  :  13  :  5  for  20  weeks,  at  5 

per  cent,  per  annum  ? 

*  ^  Ans.  £4:19:  10^. 

22.  What  is  the  amount  of  £375  :  6  :  1  for  12  weeks,  at  4^ 
per  cent,  per  annum?  ■^^^^^'  £379  :  4  :  O^. 

When  the  Interest  is  for  any  number  of  days. 

Rule.  As  365  days  are  to  the  interest  of  the  given  sum  for  a 
year,  so  are  the  .days  given  to  the  interest  required., 

23.  At  5»j  per  cent,  per  annum,  what  is  the  interest  of  £985  . 

2  .  7  for  5  years,  127  days  ? 

''  Ans.  £289  .  15  .  3. 

24.  What  is  the  interest  of  £2726  .  1  .  4  at  4^  per  cent,  per 
annum,  for  three  years,  154  days  ? 

A71S.  £419  .  15  .  6i. 

When  the  Amount,  Time,  and  Bate  per  cent,  are  given  to  find 

the  PrincijMl. 

Rule.  As  the  amount  of  £100  at  the  rate   ,nd  time  given  :  is 
to  £100  ::  so  is  the  amount  given  :  to  the  principal  required. 

25.  What  princit)al  being  put  to  interest,  will  amount  to  £402  . 
10  in  5  years,  at  3  per  cent,  per  annum  ? 

3X5  +  100=£115  .  100  .  .  402  .  10 
20  20 


2300 


8050 


100 


23l00)a050l00(£350  Ans, 


I  4|  pe 

lent,  per 

:  10. 

cks. 
sura  for 

ks,  at  5 

:  10^. 
ts,  at  4 1 
t  :  Oi. 

am  for  a 

f  £985  . 

15  .  3. 

cent,  per 

5  .  6i. 
to  find 


given  :  is 
ired. 

;o  £402  . 


Ans^ 


INTEREST. 


78 


26.  What  principal  being  put  to  interest  for  9  years,  will 
amount  to  £734  :  8,  at  4  per  cent,  per  annum  ? 

Ans.  £540. 

27.  What  principal  being  put  to  interest  for  7  years,  at  6  per 
cent  per  annum,  will  amount  to  £334  :  16  ? 

^  Ans.  £248. 

When  the  principal^  Rate  per  cent.^  aid  Amount  are  given^ 

tofivd  the  Time. 

Rule.  As  the  interest  of  the  principal  for  1  year :  is  to  1  year : : 
80  is  the  whole  interest :  to  the  time  required. 

28.  In  what  time  will  £350  amount  to  £402  .  10,  at  3  per  cent 
per  annum  ?  * 

360        As  10  .  10  :  1  : :  52  .  10  :  6 
8  20  20 


10)60 
20 


210        2110)10510(5  years.        Ans.  402  .  10 
106  350.10 


lOlOO  52.10 

29.  In  what  time  will  £540  amount  to  £734  :  8,  at  4  per  cent 
per  annum?  uItw.  9  years. 

30.  In  what  time  will  £248  amount  to  £334  :  16,  at  6  per 
cent  per  annum  ?  -^''^'  '  years. 

Whm  the  Principal,  Amount,  and  Time,  are  given,  to  find  the 

Bate  per  cent. 

Rule.  As  the  principal :  is  to  the  interest  for  the  whole  time  :  : 
8i>  is  £100  :  to  the  interest  for  the  same  time.  Divide  that  in- 
terest by  the  time,  and  the  quotient  will  be  the  rate  per  cent. 

31.  At  what  rate  per  cent  will  350  amount  to  £402  :  10  in 

5  years'  time  ? 

.350  As  350  :52  .  10::  100:  £15 
20 


52.10 


1050 
100 


36i0)i0500»O(00O8.  =  £l5-7-6^3  per  ctMit. 
32.  At  what  rate  per  cent  will  £248  amount  to  £334  :  10  in 
7  years' time?  -'^"*-  ''  per  cui-.t.     ; 


H 


74 


INTEKEST. 


» 


; 


■^ 


33.  At  what  ra^te  per  cent,  will  £540  amount  to  £784  :  8  in  9 
years' time?  '  ^»w.  4  per  cent. 

COMPOUND  INTEREST, 

Is  that  which  arises  both  from  the  principal  and  interest;  that 
is,  when  the  interest  on  money  becomes  due,  and  not  paid,  the 
same  interest  is  allowed  on  that  interest  unpaid,  as  was  on  the 
principal  before. 

Rule  1.  Find  the  first  years'  interest,  which  add  to  the  princi- 
pal ;  then  find  the  interest  of  that  sum,  which  add  as  before,  and 
so  on  for  the  number  of  years. 

2.  Subtract  the  given  sum  from  the  last  amount,  and  it  will 
give  the  compound  interest  required. 

EXAMPLES. 

1.  What  is  the  compound  interest  of  £500  forborne  3  years, 
at  5  per  cent,  per  annum  ? 

500     500  525 

6       25  26  . .  5  « 


25100 


525 = 1st  year.  55 1 . .  5 = 2d  year. 

5  6 

651..  5 

26125  27156..  5     2Y.11..3 


20 


20 


5100 


11125 
12 

3100 


578.16..3=3dyear. 
600  prin.  sub 


78  .  16  . .  3=inter.for3years. 


2.  What  is  the  amount  of  £400  forborne  3^  years,  at  6  per 
cent,  per  annum,  compound  interest?         Ans.  £490  :  13  :  11^. 

3.  What  will  £650  amount  to  in  5  years,  at  5  per  cent,  per 
annum,  compound  interest?  Ans.  £829  :  11  :  7^. 

4.  What  IS  the  amount  of  £550  :  10  for  3  years  and  6  juionths, 
at  6  per  cent,  per  annum,  compound  interest  ? 

^w5.  £f>"5  :6j,5. 

5.  What  is  the  compound  interest  of  £764  for   ■  years 'and  9 
months,  at  6  per  cent,  per  annum?  Am,  £24.-     18  :  8. 

6.  What  is  the  compound  interest  of  £67  :  10  :  a  ft?  a  years, 
7  months,  and  15  days,  at  6  per  cent,  per  annum? 

Ans,  £18  ;  o  :  Sjf, 


BEBATE   OR  DISCOUNT. 


^ 


:8m  9 
r  cent. 


7.  What  is  tlie  compound  interest  of  £259  :  10  for  3  years,  9 
months,  and  10  days,  at  4^  per  cent,  per  annum  ? 

Ans.  £46  :  19  :  10^. 


est;  that 
paid,  the 
s  on  the 


16  pnnca- 
sfore,  and 

id  it  will 


3  years, 


REBATE  OR  DISCOUNT, 

Is  the  abating  of  so  much  money  on  a  debt,  to  be  received  be- 
fore it  is  due,  as  that  money,  if  put  to  interest,  would  gain  in  the 
same  time,  and  at  the  same  rate.  As  £100  present  money  would 
discharge  a  debt  of  £105,  to  be  paid  a  year  to  come,  rebate  bemg 
made  at  6  per  cent. 

Rule.   As  £100  with  the  interest  for  the  time  given  :  is  to 
Oiat  interest : :  so  is  the  sum  given  :  to  the  rebate  required. 

Subtract  the  rebate  from  the  given  sum,  and  the  remainder 
^dll  be  the  present  worth. 

EXAMPLES. 


P. 


ar  3  years. 

at  6  per 

I :  Hi. 

cent,  per 
1  :7i. 
6  months, 

:  6/.  5. 
ars'and  9 
18  :  8. 
y  a  years, 

3  ;8i 


1.  'WTiat  is  the  discount  and  present  worth  of  £487  :  12  for  6 
months,  at  3  per  cent,  per  annum  ? 


fm=i6 


3 

100 

103 


As  103:0::487:12 
20     20 


2060 


9752 
3 


-£  8. 


487  :  12  principal. 
14 :    4  rebate. 


20610)292516(14  .  4  rebate. 
206 


Ans.  £4:1  Z'.    8  present  worth. 


865 
824 


416==4s. 


2    What  is  the  present  payment  of  £357':  10,  which  \y&& 
agreed  to  be  paid  9  months  hence,  at  5  per  cent,  per  aniiiim  ?  ^ 


jins\  ^o=it  .  IX 


3.  What  is  the  discount  of  £275  :  10  for  7  months,  at  6  per 


cent  per  annum  ? 


Ans.  £7  :  16  :  If. 


g2 


76 


EQUATION   OF    PAYMENTS. 


I  '' 


i 


i 

i- 

i  . 


4.  Bought  goods  to  the  value  of  £109  :  10,  to  be  paid  at  nine 
months,  what  present  money  will  discharge  the  same,  if  I  am  al- 
lowed 6  per  cent,  per  annum  discount  1 

Ans.  £104  :  15  :  8^. 

5.  What  is  the  present  worth  of  £521  :  9  :  1,  payable  1  months 
hence,  at  4^  per  cent.  ?  Am.  £514  :  13  :  lOf. 

6.  What  is  the  discount  of  £85  :  10,  due  September  the  8th, 
this  being  July  the  4th,  rebate  at  5  per  cent,  per  annum  ? 

Ans.  15s..  3fd. 

I.  Sold  goods  for  £875  :  5  :  6,  to  be  paid  6  months  hence, 
what  is  the  present  worth  at  4^  per  cent.  ? 

Ans.  £859  :  3  :  4. 

8.  What  is  the  present  worth  of  £500,  payable  in  10  months, 
at  5  per  cent,  per  annum  ?  Ans.  £480. 

9.  How  much  ready  money  can  I  receive  for  a  note  of  £75, 
due  15  months  hence,  at  5  per  cent.  ? 

Ans.  £70  :  11  :  9^. 

10.  What  will  be  the  present  worth  of  £150,  payable  at  3 
four  months,  i.  e.  one  third  at  four  months,  one  third  at  8  months, 
and  one  third  at  12  months,  at  5  per  cent,  discount? 

Ans.  £145  :  3  :  8^. 

II.  Sold  goods  to  the  value  of  £575  :  10,  to  be  paid  at  2  three 
months,  what  must  be  discounted  for  present  payment,  at  5  per 
;ent.?  ^n«.  £10  :  11  :  4|. 

12.  What  is  the  present  worth  of  £500  at  4  per  cent.,  £100 
being  to  be  paid  down,  and  the  rest  at  2  six  months  ? 

Ans.  £488  :  7  :  8^. 


EQUATION  OF  PAYMENTS, 


*' 


Is  when  several  sums  are  due  at  different  times,  to  find  a  mean 
time  for  paying  the  whole  debt ;  to  do  which  this  is  the  common, 

Rule.  Multiply  each  term  by  its  time,  and  divide  the  sum 
of  the  products  by  the  whole  debt,  the  quotient  is  accounted  the 
mean  time. 


^P^i  WM— 


BQUATIOPJ   OF   PAYMENTS. 


W 


EXAMPLES. 

1  A  owes  B  £200,  whereof  £40  is  to  be  paid  at  3  months, 
£60  at  6  months,  and  £100  at  10  months;  at  what  time  may  the 
whole  debt  be  paid  together,  without  prejudice  to  either? 


£ 

40  X 

60  X 

100  X 


m. 

3 

5 

10 


120 

300 

1000 


2100)14120 

7  months  yV* 

2  B  owes  C  £800,  whereof  £200  is  to  be  paid  at  3  monOis, 
£100  at  4  months,  £300  at  5  months,  and  £200  at  6  months ; 
but  they  agreeing  to  make  but  one  payment  of  the  whole,  1  de- 
mand what  time  that  must  be  ?  ,     , «  j 

Ans.  4  months,  18  days. 

3.  I  bouffht  of  K  a  quantity  of  goods,  to  the  value  of  £360 
which  was  to  have  been  paid  as  follows:  £120  at  2  months,  and 
£200  at  4  months,  and  the  rest  at  5  months;  but  they  afterwards 
agreed  to  have  it  paid  at  one  mean  time ;  the  time  is  demanded. 
^  ^  Ans.  3  months,  13  days. 

4.  A  merchant  bought  goods  to  the  value  of  £500,  to  W  £100 
at  the  end  of  3  months,  £150  at  the  end  of  6  months,  and  £250  at 
the  end  of  12  months;  but  afterwards  they  agreed  to  discharge 
the  debt  at  one  payment ;  at  what  time  was  this  payment  made  i 

^  Ans.  8  months,  12  days. 

6.  H  is  indebted  to  L  a  certain  sum,  which  is  to  be  paid  at  6 
different  payments,  that  is,  i  at  2  months  i  at  3  months,  ^  at  4 
months,  i  at  5  months,  i  at  6  months,  and  the  rest  at  7  months, 
but  they  agree  that  the  whole  should  be  paid  at  one  equated  time; 

what  is  that  time  ?  ^       .         .i      i        >+„.. 

Ans.  4  months,  1  quarter. 

6.   A  is  indebted  to  B  £120,  whereof  i  is  to  be  paid  at  3 

"•    -^  .,  1    ii.  - i.   «*    n   -M^/^ntKc.  •   what.  IS  the 

months,  ^  at  6  moutns,  ana  luu  ict^u  »^  o-  x^v..vx,.,   

equated  time  of  the  whole  payment?       ^^  ^  ^^^^^  ^  ^^^ 

e3 


mill  iiii>i 


78 


BABTER. 


BARTER 


is  the  exchanging  of  one  cc-  ,    for  another,  and  informs 

the  traders  so  to  proporti'^iK\te  their  goods,   that  neither  may 
sustain  loss. 

Rule  1st.  Find  the  vahie  of  that  commodity  whose  quantity 
is  given ;  then  find  what  quantity  of  the  other,  at  the  rate  pro- 
posed, you  may  have  for  the  same  money. 

2dly.  When  one  tn^s  goods  at  a  certain  price,  ready  mone), 
but  in  bartering,  advancu  it  to  something  more,  find  what  the 
other  ought  to  rate  his  goov.  at,  in  proportion  to  that  advance, 
and  then  proceed  as  before. 

EXAMPLES. 


1.  What  quantity  of  chocolate,  at 
4s.  per  lb.  must  be  delivered  in  barter 
for  2  cwt.,  of  tea,  at  93.  per  lb.  i 
2  cwt, 
112 

2241b. 
9  price. 

4)2016  the  value  of  the  tea. 

504  lb.  of  chocolate. 


■'^1 

t' 


2.  A  and  B  barter ;  A  hath  20  cwt 
of  prunes,  at4d.  per  lb.  ready  money, 
but  in  barter  will  have  5d.  per  lb.  and 
B.  hath  hops  worth  328.  per  cwt., 
ready  money ;  what  ought  B.  to  rat^ 
his  hops  at  in  barter,  and  what  quan- 
tity must  bfi  given  for  the  20  cwt,  of 
prunes  ? 

112        As  4:  5::  32 
20  5 


8. 

40 
12 


2240 
5 

cwt  qr.  lb. 

4810)112010(23  .  1 


4)160 
408. 


96 

160 
144 

16=1  qr.  9  lb.  j| 


9Jf .  J?n#. 


3.  How  much  tea,  at  9s.  per  lb.  can  I  have  in  barter  for  4  cwt,  2qrg. 
of  chocolate,  at  4s.  per  lb.  ? 

^ns.  2  cwt 

4.  Two  merchants  barter ;  A  hath  20  cwt.  of  cheese,  at  21s.  6d.  per  cwt; 
B  hath  8  pieces  of  Irish  cloth,  at  £3  .  148.  per  piece :  1  desire  to  know  who 
must  receive  the  difference,  and  how  much  ? 

^n«.  B.  must  receive  of  A  JBS  .  2. 

5.  A  and  B  barter ;  A  hath  3h  lb.  of  pepper  at  13 id.  per  lb. ;  B  hath  gin- 
ger at  154d.  per  lb.;  how  much  ginger  must  he  deliver  in  barter  for  the 
pepper  .'  ^ns.  3  lb.  1  oz.|f 


«.  He 
in  barte 

7  Al 
him  £1 
The  qut 

8.  A 
for  whic 
lb. ;  I  d 

9.  If 
lb.  of  to 

10.  C 
have  8s 
how  mu 
lent  wit 

Is  a  Ri 
of  gOO( 
gain  so 

The 


i  1.  If 
lis.  and 
gain  pel 


12 
11 


^'^^siinMt"- 


PBOFIT   AND   LOSS. 


79 


6.  TTow  many  dozen  of  candles,  at  59.  2d.  per  dozen,  must  be  delivered 
Id  barter  for  three  cwt.  2  qrs.  16  lb.  of  tallow,  at  379  4d.  per  cwt.  ? 

Ana.  26  dozen  3  lb.|  j 

7  A  hath  609  yards  of  cloth,  worth  Ha.  per  vard,  for  which  B  giveth 
him  £123  .  12.  in  ready  money,  and  S5  cwt.  2  qrs.  24  lb.  of  bees'-wax. 
The  question  is,  what  did  B  reckon  his  bees'-wax  at  per  cwt.  ? 

Ans.  £3  .  10. 

8.  A  and  B  barter  ;  A  hath  3-^0  dozen  of  candles,  at  4s.  6d.  per  dozen  ; 
for  w^hich  B  giveth  him  £30  in  money,  and  the  rest  in  cotton,  at  8d.  per 
lb. ;  I  desire  to  know  how  much  cotton  B  gave  A  besides  the  money  ? 

Jlns.  11  cwt.  1  qr. 

9.  If  B  hath  cotton,  at  Is.  2d.  per  lb.,  how  much  must  he  give  A  for  114 
lb.  of  tobacco,  at  6d.  per  lb. 

Ana.  48  lb. jf. 

10.  C  hath  nutmegs  worth  7s.  nd.  per  lb.  ready  money,  but  in  barter  will 
have  8s.  per  lb. ;  and  D  hath  leaf  tobacco  worth  9d.  per  lb.  ready  nioney ; 
how  much  must  D  rate  his  tobacco  at  per  lb.  that  his  profit  may  be  equiva- 
lent with  C's  i 

'     Ana.  9id.  U- 


4)160 
408. 


3S 

■IT 


PROFIT  AND  LOSS 

la  a  Rule  that  discovers  what  is  got  or  lost  in  the  buying  or  selling 
of  goods,  and  instructs  us  to  raise  and  lower  the  price,  so  as  to 
gain  so  much  per  cent,  or  otherwise. 

The  questions  in  this  Rule  are  performed  by  the  Rule  of  Three. 


EXAMPLES. 


Ji  1.  If  a  yard  of  cloth  is  bought  for 
Us.  and  sold  for  12s.  6d.  what  is  the 
gain  per  cent.  ? 

As  11  :  1  : P  :  :  100 
12  20 


18 


12.6 
11.0 

1.6 


2000 
18 

11)36000 


12)3272y\ 
210)2712 . 8 


Ans.  £13  .  12  .  8j\ 


2.  If  60  ells  of  Holland  cost  £18 
what  must  1  ell  be  sold  for  to  gain  8 
per  cent.  ? 

As  100  :  IS  :  :  108 
108 


1100)19144 
20 


8180 
12 


9160 


12X5=60 

12)19  .    8  .  9i 

5)1  .  12  .  41 

0.    6.51 


2140 


-Ans.  6s.  5|d 


■?1 


80 


FELLOWSHIP. 


what 


3.  If  1  lb.  of  tobacco  co'st  16d.  and  is  sold  for  20d.  what  is  the  gain  per 

lie  a  parcel  of  cloth  be  sold  for  £500.  and  at  12  per  cent,  gain,  what 

""''lVa'"a?d'of  cloth  is  bought  for  13s.  4d.  and  sold  again  ^o^^\^^^:^^-^ 

'"  'e'  If  U2Tb'of  iL  cost  27s.  Gd..  what  must  1  cwt.  be  sold^fi^  to^in 
I'inercent  >  •^"■'-  ■^l  •  1^  •  ^* 

7    If  375  yards  of  broad  cloth  be  sold  for  £490,  and  20  per  cent,  profit, 

-^"^  rctr;/H.s,  for  £3  .  .5,  at  .he  rate  of  ^S^e.  ce;„   p,.fit, 
,at  would  have  been  the  gain  per  cent,  if  1  had  sold  them  for  £8  pel  cv%  t. . 

^ns.  dL4S  .  A  •  Ala- 

9    If  90  ells  of  cambric  cost  £G0,  how  much  must  1  sell  it  per  yard  to 
,Q  i  J  Jlns.  r2s.  7(1. 

^*10.  A^pl'umber  sold  10  fother  of  lead  for  £204  .  15,  (the  fother  being  lOi 
cwt.)  and  gained  after  the  rate  of  £12  .  10  percent.  ;  what  did  »  cost  him 
'       J  ^  Ans.  18s.  8d. 

^^^Ir'^Bought  43G  yards  of  cloth,  at  the  rate  of  Ss.  6d.  per  yard,  and  sold 
it  for  lOs.  4d.  per  yard ;  what  was  the  gain  of  the  whole  ? 

12    Paid  £09  for  one  ton  of  steel,  which  is  retailed  at  Gd.  per  lb. ;  what 
is  the  profit  or  loss  by  the  sale  of  15  tons.  -^ns.  £182  loi^s. 

13.  Bought  124  yards  of  linen,  for  £32 ;  how  should  the  same  he  retailed 
per  yard  to  gain  15  per  cent.  ?  -^^s-  os.  lld.y^j. 

14.  Bought  249  yards  of  cloth,  at  3s.  4d,  per  yard,  retailed  the  same  at 
48.  2d.  per  yard,  what  is  the  profit  in  the  whole,  and  how  much  per  cent.  .' 

*^     "^  Am.  £10  .7.6  proUt,  and  25  per  cent. 

FELLOWSHIP 

&  when  two  or  more  join  their  stock  and  trade  together,  so  to 
determine  each  person's  particiilar  share  of  the  gain  or  loss,  in 
proportion  to  his  principal  in  joint  stock.  m\ 

By  this  rule  a  bankrupt's  estate  may  be  divided  amongst  his 
creditors ;  as  also  legacies  may  be  adjusted  when  there  is  a  de6- 
ciency  of  assets  or  eflfects. 

FELLOWSHIP    IS    EITHER   WITH    OR   WITHOUT   TIME. 

FELLOWSHIP  WITHOUT  TIME. 

Rule.  As  the  whole  stock :  is  to  the  whole  gain  or  loss  :  :  m 
is  each  man's  share  in  stock  :  to  his  share  of  the  gain  or  loss. 

Proof.  Add  all  the  shares  together,  and  the  sum  v\  i!i  be  equJi 
to  the  given  gain  or  loss— but  the  surest  way  is,  as  tlif  wholf 
gain  or  loss :  is  to  the  whole  stock  :  :  so  is  each  man's  share  of 
the  gain  or  loss  :  to  his  share  in  stock. 


C 


FELL0W8HIF. 


81 


HI 


e  gain  per 
*.  £-25. 
;ain,  what 
(   £500. 
108.  what 

t*.  mo. 

for  to  gain 

11  .  7i 
jnt.  profit, 

.  1  .  Oi 
»nt.  profit, 
I  per  cwt. .' 

2.  Hi 
)er  yard  to 

123.  7d. 
r  being  19i 
it  cost  him 

183.  8d. 
d,  and  sold 

.  19  .  4. 
r  lb.  ;  what 
182  loss. 
!  be  retailed 

lid    2_8 

the  same  at 
1  per  cent.  ? 
per  cent. 


:,her,  so  to 
or  loss,  in 

I 

nongst  his 
e  is  a  defi- 


lE. 


r  loiis  :  :  fO 

W  loSifl. 

. ..  «  « 

lii  iKi  «q51J.i 
the  wholf 
's  share  of 


EXAMPLES 

1.  Two  merchants  trade  together;  A  puts  into  stock  £2C,  and  B  JC40| 
they  gained  £30;  what  is  each  person's  share  thereof? 


A  60  :  50  :  :  20 

20 

610)10010 
£1G  .  13  .  4 


20+40=00 
As  60  :  00  I  :  40 

40 

« 

610)20010 


33  .    6.8,  B'»  share. 
16  .  13  .  4,  A's  share. 


50  .    0.0  proof. 


£33  .  6  .  S 


2.  Three  merchants  trade  together.  A,  B,  and  C  A  puts  in  £20,  B  £30, 
and  C  £40  ;  they  gained  £180 :  what  is  each  man's  part  of  the  gain  ? 

Ans.  A  £40 ;  B  £00 ;  C  £80 

* 

3.  A,  B,  and  C,  enter  into  partnership  ;  A  puts  in  £364,  B  £482,  and 
C  £500 ;  and  they  gained  £867  ;  what  is  each  man's  share  in  proportion 
to  his  stock  ? 

Arts.  A  £234  .  9  .  34— rem.  70 ;  B  £310  .  9  .  5— rem.  248 ; 
C  £322  .  1  .  3i— rem.  1028. 

.  4.  Four  merchants,  B,  C,  D,  and  E  make  a  stock  ;  B  puts  in  £227,  C 
£349,  D  £115,  and  E  £439  ;  in  trading  they  gained  £42S  :  I  demand  each 
merchant's  share  of  the  gain  ? 

Ans.  B  £85  .  19  .  6|— 690 ;  C  £132  .  3  .  9—120 ;  D.  £43  . 
11  .  11—250 ;  E  £166  .  5  .  64—70. 

5.  Three  persons,  D,  E,  and  F,  join  in  company  ;  D's  stock  was  £750, 
E's  £460,  and  F's  £500 ;  and  at  the  end  of  12  months  they  gained  £684: 
Trhat  is  each  man's  particular  share  of  the  gain  ? 

Ans.  D  £300,  E  £184,  and  F.  £200. " 

.      6.  A  merchant  is  indebted  to  B  £275  .  14,  to  C  £304  .  7,  to  D  £152, 
^and  to  E  £104  .  6 ;  but  iipon  his  decease,  his  estate  is  found  to  be  worth 
but  £075  .  15 :  how  must  it  be  divided  among  his  creditors  ? 

Ans.  B's  share  £222  .  15  .  2—6584  ;  C's  £245  .  18  .  U— 15750  • 
D's  £122  .  16  .  21—12227  ;  and  E's  £84  .  5  .  5—15020. 

7.  Four  persons  trade  together  in  a  joint  stock,  of  which  A  has  i,  B  |, 
C  |,  and  D  | ;  and  at  the  end  of  6  months  they  gain  £100 :  what  is  each 
man's  share  of  the  said  gain  ? 

Ans.  A  £35  .  1  .  9—48 ;  B  £26  .  6  .  3^-36 ;  C  £21  .  1  .  Oi 
• ;     .  —120 ;  and  D  £17  .  10  .  10^—24. 

8.  Two  persons  purchased  an  estate  of  £1700  per  annum,  freehold,  for 
£27.200,  when  money  was  at  6  per  cent.  interest.''ARd^«t.  per  pound,  land- 
tpc ;  whereof  D  paid  £15,000,  and  E  the  rest ;  80metr«7e  after,  the  interest 
«f  the  money  falling  to  5  per  cent,  and  28.  per  poiind  land-tax,  they  sell 
the  said  estate  for  24  pears'  purchase :  I  desire  to  kno^  each  person's  shai  e  ? 

Ans.  D  £22,500 ;  E  £18,300. 


i*iif  ...Ilia 


m 


FELLOWSHIP. 


9  D  E  and  F,  join  their  stocks  in  trade ;  the  amount  of  their 
stocks  is  £647,  and  they  are  in  proportion  as  4,  6  and  8  ^e  to 
one  another,  and  the  amount  of  the  gain  is  equal  U>  Ds  stock, 
what  is  each  man's  stock  and  gain  ? 

Ans.  D's  stock  £143  .  15  .  6||  gain,  31  .  19  .  Oif 
E'8....o-  215  .  13  .  4  ....  47  .  18.  6|f 
Ps 287  .  11  .  lA 63  .  18  .  OJ/7. 

10  D  E,  and  F,  join  stocks  in  trade;  the  amount  of  their 
stock'  wal  £100 ;  D's  gain  £3,  E's  £5,  and  F's  £8  :  what  was 

each  man's  stock ?  ^  ,  t^,    r>^r, 

Ans.  D's  stock  £18  .  15 ;  E's  £31  .  5 ;  and  Fs  £50. 


FELLOWSHIP   WITH  TIME. 

in- 

Rule.  As  the  sum  of  the  products  of  each  man's  money  and 
time  :  is  to  the  whole  gain  or  loss  :  :  so  is  each  mans  product : 
to  his  share  of  the  gain  or  loss. 

P]»ooF.  As  in  fellowship  without  time. 


EXAMPLES. 


I   I 


I  <h 


1.  D  and  E  enter  into  partnership;  D  puts  in  £40  for  three 
months,  and  E   £76   for  ic^v  months ;  and  they  gained  £70  : 

what  is  each  man's  share  of  tlie  gain?  t^  n-^ 

.^W5.  D  £20,  E  £oO. 


40X3  =  120 
75X4=300 


As  420  :  70  :  :  120 
120 


As  420  :  70  :  :  300 
300 


420 


4210)84010(20 

.\        840 


4210)210010(50 
2100 

, — 4— 


2.  Three  merchants  join  in  company;  D  puts  m  stock  £l95 
14.  for   three  months,  E  £169  .  18  .  3,  for   5   months,   im\   V 
£50  .  1*'.  10,  for  11  months;  they  giuned  £364  ,  18  t  what  is 
man'i 


each 


part 


gam  I 


Ans.  D's  £fim 


0  .  A — 5008 ;  E's  £148  .  1  .  1|— 


482802;  and  Ps  £114  .  10  .  6^—14707. 


ALLIGATION. 


8S 


it  of  their 

8  are  to 

)'s  stock: 


it  of  their 
what  was 

^'s  £50. 


ncney  and 
product : 


3.  Three  merchants  join  in  company  for  18  months;  D  put  in 
£600,  and  at  five  months'  end  takes  out  £200 ;  at  ten  months' 
end  puts  in  £300,  and  at  the  end  of  14  months  takes  out  £130 : 
E  puts  in  £400,  and  at  the  end  of  3  months  £270  more ;  at  9 
months  he  takes  out  £140,  but  puts  in  £100  at  the  end  of  12 
months,  and  withdraws  £99  at  the  end  of  15  months :  F  puts  in 
£900,  and  at  6  months  takes  out  £200 ;  at  the  end  of  11  months 
puts  in  £500,  hut  takes  out  that  and  £100  more  at  the  end  of  13 
months.  They  gained  £200 :  I  desire  to  know  each  man's  share 
of  the  gain  ? 

Ans.  D  £60  :  7  :  6—21720;  E  £62  :  12  :  5^—29859;  and 
F  £87  :  0  :  0^—14167. 

4.  D,  E,  and  F,  hold  a  piece  of  ground  in  common,  for  which 
they  are  to  pay  £36  :  10  :  6.  D  puts  in  23  oxen  27  days;  E  21 
oxen  35  days;  and  F  16  oxen  23  days.  What  is  each  man  to 
pay  of  the  said  rent  ? 

Ans.  D  £13  :  3  :  1^—624;  E  £15  :  11  :  5—1688;  and  F 
£7  :  15  :  11—1136. 


D  for  three 
ined  £70  : 


ALLIGATION 


ALLIGATION  IS  EITHER  MEDIAL   OR   ALTERNATE. 


E£50. 

70  :  :  300 
300 


ALLIGATION  MEDIAL 


210010(50 

2ior     ': 

:ock  £195 
hs,   Mixi   F 
8  t  wliiiC  is 

5.1.  1|— 
-14707. 


Is  when  the  price  and  quantities  of  several  simples   are  given 
to  be  mixed,  to  find  the  mean  price  of  that  mixture. 

Rule.  As  the  whole  composition  :  is  to  its  total  value  :  :  so 
is  any  part  of  the  composition  :  to  its  mean  price.  ^ 

,^' 
the  mean  rate, 
d  quantities  at 


Proof. 


mixture 


agrees 


their  respective  prices,  the  work  is  right. 


84 


A.LLIGAT10W. 
EXAMPLES. 


1.  A  farmer  mixed  20  bushels  of  wheat,  at  Ss.  per  bushel,  and 
36  bushels  of  rye,  at  3s.  per  bushel,  with  40  bushels  of  barley, 
at  2s.  per  bushel.  I  desire  to  know  the  worth  of  a  bushel  of 
this  mixture. 

As  96  :  288  :  :  1  :  3 


20X5  =  100 
30X3  =  108 
40X2=   80 


96 


288 


Ans.  3s. 


•2.  A  vintner  mingles  15  gallons  of  canary,  at  8s.  per  gallon, 
with  20  gallons,  at  7s.  4d.  per  gallon,  10  gallons  of  sherry,  at  6s. 
8d.  per  ^fallou,  and  24  gallons  of  white  wine,  at  4s.  per  gallon. 
What  is  the  worth  of  a  gallon  of  this  mixture  ? 

Ans.  6s.  2^d.-JA. 

3.  A  grocer  min^ded  4  cwt.  of  sugar,  at  5."s.  per  cwt.  with  1 
cwt.  at  43s.  }<er  cwt.  and  6  cwt.  at  37s.  per  cwt.  I  demand  the 
price  of  2  cwt.  of  this  mixture  ?  Ans.  £4.8.9. 

4.  A  malster  ^ningles  30  quarters  of  brown  malt,  at  28s.  per 
quarter,  \vith  lO  quarcers  of  pale,  at  30s.  per  quarter,  and  24 
quarters  of  high-dried  ditto,  at  25s.  per  quarter.  What  is  the 
value  of  8  bushels  of  this  mixture  3 

Ans.  £1.8.  2^d.TV. 

5.  If  I  mix  27  bushels  of  wheat,  at  5s.  6d.  p3r  bushel,  with 
the  same  quantity  of  rye,  at  4s.  per  bushel,  and  14  bushels  of 
barley  at  2s.  8d.  per  bushel,  what  is  the  worth  of  a  bushel  of  this 

mixture?  Ans.  is.  SU-U- 

6.  A  vintner  mixes  20  gallons  of  port  at  5s.  4d.  per  gallon, 
with  12  gallons  of  white  wine,  at  5s.  per  gallon,  30  gallons  of 
Lisbon,  at  Os.  per  gallon,  and  20  gallons  of  mountain,  at  4s.  6d. 
per  gallon.     What  is  a  gallon  of  this  mixture  worth  ? 

Ans.  5s.  3|d.ff. 

7.  A  refiner  having  12  lb.  of  silver  bullion,  of  6  oz.  fine,  would 
melt  it  with  8  lb.  of  7  oz.  fine,  and  10  lb.  of  8  oz.  fine;  required 
the  fineness  of  1  lb.  of  that  mixture  ? 

A^t.    6  oz.  18  dwts,  16  g^ 

8.  A  tobacconist  would  mix  50  lb.  of  tobacco,  at  lid.  per  Id. 
with  30  lb.  at  14d.  per  lb.,  25  11.  at  £2(i.  per  lb.  and  37  lb.  at  2s. 
per  lb.    What  will  1  lb.  of  this  mixture  be  worth  ? 

Am,  16|d.  IH- 


22: 


jmy- 


.■y^gP*'"*'**""      * 


ALLrSATION. 


85 


ALLIGATION  ALTERNATE 


hel,  and 
'  barley, 
ishel  of 


•  gallon, 
y,  at  6s. 
r  gallon, 

.  with  1 
aand  the 

8  .  9. 
28s.  per 

and   24 
,t  is  the 

tiel.  with 
isliels  of 
si  of  this 

r  gallon, 
aliens  of 
t  4s.  6d. 

ad  AA 
le,  would 
required 

16  g-. 
I,  per  iD. 
lb.  at  2s. 

d.  IH. 


Is  when  the  price  of  several  things  are  given 
ties  of  them  to  make  a  mixture,  that  ma 
pounded. 

In  ordering  the  rates  and  the  given  price,  observe, 
1.  Place  them  one  under  the  other,       18 — . 
and  the   propounded   price  or  mean  ^oSO— [ 
rate  at  the  left  hand  of  them,  thus,       24_l 

28_ 


find  such  quanti- 


bear  a  price  pro- 


2 

6 

4 

2 

2.  Link  the  several  rates  together  by  2  and  2,  always  observ- 
ing to  join  a  greater  and  a  less  than  the  mean. 

3.  Against  each  extreme  place  the  difference  of  the  mean  and 
its  yoke  fellow. 

When  the  prices  of  the  several  simples  and  the  mean  rate  are 
given  without  any  quantity,  to  find  ho\v  much  of  each  simple  is 
required  to  compose  the  mixture. 

Rule.  Take  the  difference  between  each  price  and  the  mean 
rate,  and  set  them  alternately,  they  will  be  the  answer  required. 

Proof.  By  Alligation  Medial. 

EXAMPLES. 

1.  A  vintner  would  mix  four  sorts  of  wine  together,  of  18d., 
20d.,  24d.,  and  28d.  per  quart,  what  quantity  of  each  must  he 
have,  to  sell  the  mixture  at  22d.  per  quart? 


22 


Answer.  Proof. 

18 ,2  of  18d.  =     36d. 

6  of  20d.  =  120 
4  of  24d.  =  96 
2  of  28d.  =     56 


20 

24 


28_J 


14 


)808 
22d. 


22 


Proof. 
=  108d. 
2  of  20d.  =     40 
2  of  24d.  =    48 
4  of  28d.  =  112 


or  thus, 

18 6  of  isa 

20 

24_l 
28 


U 


)308 
22d. 


NoTK.   Qiiestions  in  this  rule  admit  of  a  great  variety  of  an 
Bwers,  according  to  the  manner  of  hnkin^     aem. 

2.  A  jxi'ocer  would  mix  sugar  at  4d.,  od.,  and  lOd.  p( 
as  to  sell  the  compound  for  8d.  per  lb.;  what  quantity 


so 


must  he  take  ? 


each 


Arts.  2  lb.  at  4d.,  2  lb.  at  Od.,  and  6  lb.  at  lOd. 


86 


ALLIGATION   PARTIAL. 


3  I  desiro  to  know  how  miicli  tea,  at  16s.,  14s.,  9s.,  and  83 
per  lb.,  will  compose  a  mixture  worth  10s.  per  Ih.  ? 

^         Ans.  1  lb  at  16s.,  2  lb.  Us.,  6  lb.  at  9s.,  and  4  lb.  at  8s 

4  A  farmer  would  mix  as  much  barley  at  3s.  6d.  per  busheV 
we  at  4s  per  bushel,  and  oats  at  2s.  per  br  hel,  as  to  make  a 
„^n^tm-e  wo?th  2s.  ed.  per  bushel.     How  much  is  that  of  each 

'""'^ '  Ans.Q  bushels  of  barley,  6  of  rye,  and  30  of  oats. 

5  A  grocer  would  mix  raisins  of  the  sun  at  Td.  per  lb.,  with 
Malagtslt  6d.,  and  Smyrnas  at  4d^  per  1^  I Jesire^t^^^^^^^^ 

what  quantity  of  each  sort  he  must  take  to  sell  them  at  5d.  per  lb. . 
What  quani  y  ^^^^  ^  ^^  ^^  ^^.^.^^^  ^^  ^^^  ^^^^  ^  j^^  ^^  mi^gas, 

and  3  lb.  of  Smyrnas.  j  i     o  i 

6.  A  tobacconist  would  mix  tobacco  at  2s.,  Is  6d.,  and  Is.  3d. 
per  lb.,  so  as  the  compound  may  bear  a  price  of  Is.  8d.  per  ID. 
What  quantity  of  each  sort  must  he  take?^        ..,,..     oj 
Ans.  1  lb.  ^.  2s.,  4  lb.  at  Is.  6d.,  and  4  lb.  at  Is.  3d. 

ALLIGATION  PARTIAL, 

T.  when  the  prices  of  all  the  simples,  the   quantity  of  but  one 
•   of  Them  ^d  L  mean  rate  are  given  to  find  the  several  quanti- 
ties of  the  rest  in  proportion  to  that  given. 

Rule.  Take  the  difference  between  each  price  and  the  mean 

ns'thf^ke'c^f  that  simple  whose  quantity  is  ^^^^^^  to 
the  rest  of  the  differences  severally  :  :  so  is  the  quantity  given  .  to 
the  several  quantities  required. 

EXAMPLES. 

1.  A  toba^iconist  being  determined  to  mix  20  ^b- of  tobacco 
«t  Ifid  ner  lb  with  others  at  16d.  per  lb.,  18d.  per  lb.,  and  22d. 
per  tb:;C  miny  pounds  of  each  sort  must  he  take  to  make 
one  pound  of  that  mixture  worth  l7d.? 

Answer.  Proof.  ,  .  .  oa  .  a 

15 5  20  lb.  at  15d.  =  300d.    As  5  :  1  : :  20  .  4 


IV 


,wl6_. 

18_J 
22 


1    4lb.atl6d.  =    64d.    As5:l::20:4 

1  4  lb.  at  18d.  =     Viia.    as  o  ;  -  -  .  -v  .  •-• 

2  8  lb.  at  22d.  =  l'76d. 


Ans.  36  lb. 


612d. :  :  1  lb.  I'^d. 


ALLIGATION   TOTAL. 


2.  A  farmer  would  mix  20  bushels  of  wheat  at  60d.  per  bush- 
el, with  rye  at  36d.,  barley  at  24d.,  and  oats  at  18d.  per  bushel. 
How  much  must  he  take  of  each  sort,  to  make  the  composi- 
tion worth  3 2d.  per  bushel? 

Ans.  20  bushels  of  wheat,  35  bushels  of  rye,  70  bushels 
of  barley,  and  10  bushels  of  oats. 

3.  A  distiller  would  mix  40  gallons  of  French  Brandy,  at  12s. 
per  gallon,  with  English  at  Vs.-,  and  b^Avits  at  4s.  per  gallon. 
What  quantity  of  each  sort  must  he  take  to  aflford  it  for  Ss.  per 
gallon  ?  ^ 

Ans.  40  gallons  FrenJi,  32  English,  and  32  spirits. 

4.  A  grocer  would  mix  teas  at  i2s.,  10s.,  and  6s.,  with  20  lb. 
at  4s.  per  lb.  How  much  of  each  sort  must  he  take  to  make 
the  composition  worth  8s.  per  lb.  ? 

Ans.  20  lb.  at  4s.,  10  lb.  at  6s.,  10  lb.  at  10s.,  20  lb.  at  12s. 

6.  A  wine  merchant  is  desirous  of  mixing  18  gallons  of  Ca- 
nary, at  6s.  9d.  per  gallon  with  Malaga,  at  7s.  6d.  per  gallon, 
sherry  at  5s.  per  gallon,  and  white  wine  at  4s.  3d.  per  gallon. 
How  much  of  each  sort  must  he  take  that  the  mixture  may  b« 
sold  for  6s.  per  gallon  ? 

Ans.  18  gallons  of  Canary,  31|  of  Ma^uga,  13^  of  Sherry, 
and  27  of  white  wine. 


ALLIGATION  TOTAL. 


Is  when  the  price  of  each  simple,  the  quantity  to  Be  compound- 
ed, and  the  mean  rate  are  given,  to  find  how  much  of  each  sort 
will  make  that  quantity. 

Rule.  Take  the  difference  betwe  n  each  price,^  and  the  mean 
rate  as  before.    Then, 

As  the  sum  of  the  .1?  Terences  :.  is  to  each  particular  differ- 
ence :  :  so  is  the  quantliy  given  :  to  the  quantity  required. 

EXAMPLES. 
1.  A  grocer  has  four  sorts  of  sugar,  viz.,  at  12d.,  lOd.,  6d.,  and 


4d.  per  lb. :  and  would  make  a 


per 


t 


I  desire  to  know  what 


composition  of  144  lb.  worth  8d. 
quantity  of  each  he  must  take  ? 


u2 


88 


POSITION,    OK   THE    RULE    OF   FALSE. 


Ansiver. 
12 4 

— .       2 
6 

4 


Proof. 
48  at  12d.  576=: As  12 
24  at  lOd.  240=:As  12 
24  at    6d.  144=As  12 
48  at    4d.  192=As  12 


4 
2 

2 
4 


144 
144 
144 
144 


48 
24 
24 
48 


If  1 


12  144  )1152(8d. 

2  A  grocer  having  four  sorts  of  tea,  at  5s.,  6s.,  8s.,  and  9s. 
per  lb.,  wonld  have  a  composition  of  8l  lb.,  worth  7s.  per  lb. 
What  quantity  must  there  be  of  each  ?  ^  , ,  i  ik  ^f  o. 

Ans.  Uh  lb.  of  5s.,  29  lb.  of  6s.,  29  lb.  of  8s,  and  14^  lb.  of  9s. 

3  A  vintner  having  four  sorts  of  wine,  viz.,  white  wme  at  4s. 
per 'gallon;  Flemish  at  6s.  per  gallon;  Malaga  at  8s.  per  gal- 
Fon;  and  Canary  at  10s.  per  gallon;  ^^^^^  ^'^^^^.^^f ^^^J^^lf  ^^ 
of  60  gallons,  to  be  worth  5s.  per  gallon.     What  quantity  of 

each  must  hj^take?  ^^^^^^^  ^^  ^^  .^^  ^.^^^  ^  ^^^^^^^ 

5  gallons  of  Malaga,  and  5  gallons  of  Canary. 

4  A  silversmith  had  four  sorts  of  gold  viz.,  of  24  carats 
finfi*  of  ^2  20  and  15  carats  fine,  and  would  mix  as  much  ot 
tl  sorf4tWr,  so  as  to  have  42  oz.  of  17  carats  fine.     How 

much  must  he  take  of  each?  j  on  ^„ 

Ans.  4  oz.  of  24,  4  oz.  of  22,  4  oz.  of  20,  and  30  oz. 

of  15  carats  fine. 

5  A  drucrmst  having  some  drugs  of  8s.,  5s.,  and  4s.  per  lb., 
m^elhem  into  two  parcels;  one  of  28  lb.  at  6s  peHb  the 
Sher  of  4^  lb.  at  7s.  per  lb.  How  much  of  each  sort  did  he 
take  for  each  parcel  ? 

^ws.  12  lb.  of  8s.  30  lb.  of  8s. 

8  lb.  of  5s.  .       6  lb.  of  6s. 

8  lb.  of  4s.  6  lb.  of  48. 

28  lb.  at  6a.  per  lb.         42  lb.  at  7s.  per  lb. 
POSITION,  OR  THE  RULE  OF  FALSE, 

Is  a  rule  that  by  f^ilse  or  supposed  numbers,  taken  at  ple^ur^ 
discovers  the  true  one  requirei  It  is  divided  into  two  perts, 
Single  and  Double. 


m"^- 


.    -  i.- '-  3" " 


POSITION   OR   THB   BULB   OF   FALSB. 


SINGLE  POSITION, 

Is,  by  using  one  supposed  numb^,  and  working  with  it  as  tke 
true  one,  you  find  the  real  number  required,  by  the  following 

Rule.  As  the  total  of  the  errors  :  is  to  the  true  total : :  so  is 
the  suppos'^d  number  :  to  the  true  one  required. 

Proof.  Add  the  several  parts  of  the  sum  together,  and  if  it 
agrees  with  the  sum  it  is  right. 

EXAMPLES. 

•♦■■■ 

1.  A  schoolmaster  being  asked  how  many  scholars  he  had,  sfud, 
If  I  had  as  many,  half  as  many,  and  one  quarter  as  many  more, 
I  should  have  88.     How  many  had  b|j 

Suppose  he  had. .  40        As  110  : 
as  many. ...  40 
half  as  many  20 
1^  as  many  . .  10 


110 


1110)35210(32 
33 

22 
22 


88  proot 


2.  A  person  having  about  him  a  certain  number  of  Portugal 
pieces,  said,  If  the  third,  fourth,  and  6th  of  them  were  added 
together,  they  would  make  64.  I  desire  to  know  how  many  he 
had?  -Ans.  12. 

• 

3.  A  gentleman  bought  a  chaise,  horse,  and  harness,  for  £60, 
the  horse  came  to  twice  the  price  of  the  harness,  and  the  chaise 
to  twice  the  price  oi  the  hoi-se  and  harness.  What  did  he  give 
for  each  ? 

Ans.  Horse  £13  :  6  :  8,  Harness  £6  :  13  :  4,  Chaise  £40. 

4.  A,  B  and  C,  being  determined  to  buy  a  quantity  of  goods 
which  would  cost  them  £120,  agreed  aiuoiig  Iheinselvea  tnai  o 
should  have  a  third  part  more  than  A,  and  C  a  fourth  part  more 
than  B.    I  desire  to  know  what  each  man  must  pay  ? 

J»s.  A  £30,  B  £40,  0  £50. 

h3  X 


HMMM 


POSITION,   OB   THE   BULE    OF   FALSE. 

5  A  person  rlolivered  to  another  a  sum  of  money  imknown,  to 
receive  interest  for  the  same,  at  6  per  cent  per  annum,  s.-le  in- 
terest, and  at  the  end  of  10  yeat^  received,  ^r  principal  ar a  m- 
terest,  £300.     What  was  the  sum  lent ?  ^ns.  ilb7  .  lu. 

DOUBLE  POSITION, 

Is  bvmakincr  use  of  two  supposed  numbers,  and  if  both  prove 
Llsef  (L  itVnerally  happens)  they  are,  with  their  errors,  to 
be  thus  ordered : — 

EuiE  1.  Place  euch  error  against  its  respective  position. 

2  Multiply  tliem  cross-ways.  ,    \    ,       .u... 

3  K  the  erro.^  are  ahke,  i.  e.  both  greater,  or  hoth  less  than 
the  jven  number,  t-vke  their  difiference  for  a  divisor,  and  the 
^fferfn^of  the  products  for  a  dividend.  But  if  unlike  take 
S  sum  for  a  divisor,  the  sum  of  their  products  for  a  dividend, 
the  quotient  will  be  the  answer. 

EXAMPLES. 
1   A  B,  and  C,  would  divide  £200  between  them,  so  that  B 
mayhte  £6  more' than  A,  and  C.  £8  more  than  B;  how  much 

must  each  have  ?  »  ,    n    ^ 

Then  suppose  A  had  50 
then  B  must  have  56 
andC €4 


Suppose  A  had  40 
Then  B  had  46 
and  C  ....  54 


(mgik 


140  too  little  by  60. 


170  too  little  by  30. 


I 


sup.  errors. 
40  ^  60 
60  ^  30 


00 
30 


3000  1200 
1200 


60  A 
66  B 

74  0 


30  divisor.         


200  proof. 


310)18010 

60     Ans.  for  A. 
2   A  man  had  two  silver  cups  of  unequal  weight,  having  ono 
_..^:„1  wi,  .f  ..  ....  now  if  the  cover  is  put  on  the  less  cup, 

H^mlouSe  thei  wSght  of  the  greater ^cup;  ^and^set  on^u.. 
orreater 


m  the  weight  of  each  cup  ? 


Ans.  3  ounces  less,  4  greater. 


lown,  to 
. ''^  le  in- 
avxi  iu- 
7  :  10. 


■h  prove 
rrors,  to 


less  than 

and  the 

ike,  take 

dividend, 


io  that  B 
LOW  much 


EXCHANGE. 


^1 


ttle  by  30. 


3.  A  gentleman  bought  a  house,  with  a  garden,  and  a  horse  in 
the  stabb,  for  £500 ;  now  he  paid  4  times  the  price  of  the  horse 
for  the  garden,  and  5  times  the  price  of  the  garden  for  the  house. 
What  was  the  value  of  the  house,  garden,  and  horse,  separately  ? 

Ans,  horse  £20,  garden  £80,  house  £400. 

4.  Three  persons  discoursed  concerning  their  ages:  says  II, 
I  am  30  years  of  age ;  says  K,  I  am  as  old  as  H  and  ^  of  L ;  and 
says  L,  I  am  as  old  as  you  both.  What  was  the  age  of  each 
person  ? 

Ans.  H  30,  K  60,  and  L  80. 

6.  D,  E,  and  F,  playing  at  cards,  staked  324  crowns;  but  dis- 
puting about  the  tricks,  each  man  took  as  many  as  he  could :  D 
got  a  certain  number ;  E  as  many  as  D,  and  15  more;  and  F  got 
a  fifth  part  of  both  their  sums  added  together.  How  many  did 
each  get  ? 

Ans.  D  127i  E  142^,  and  F  54. 

6.  A  gentleman  going  into  a  garden,  meets  with  some  ladie-3, 
and  says  to  them.  Good  morning  to  you  10  fair  maids.  Sir,  you 
mistake,  answered  one  of  them,  we  are  not  10 ;  but  if  we  were 
twice  as  many  more  as  we  are,  we  should  be  as  many  above  10 
as  we  are  now  under.     How  many  were  they  ? 

Ans.  5. 

EXCHAXGE 


Is  receiving  money  in  one  country  for  the  sarc    value  paid  in 
another. 

The  par  of  exchange  is  always  fixed  and  certain,  it  being  the 
intrinsic  value  of  foreign  money,  compared  with  sterling;  but 
the  course  of  exchange  rises  and  falls  upon  various  occasions. 

I.  FRANCE. 


lavmg  ono 
e  less  cup, 
set  on  tao 
ip.     Whr.t 


:  greater. 


Tliey  keep  their  accounts  at  Paris,  Lyons,  and  Rouen,  in  livres, 
sols,  and  deniei's,  and  exchange  by  the  crown = 4s.  6d.  at  par. 

Note.  12  deniers  make  1  sol. 

20  sols 1  hvre. 

3  Hvres ......  1  crown. 


02 


EXCHANGE. 


To  change  French  into  Sterling. 
Rule.  As  1  crown  :  is  to  the  given  rate  :  :  so  is  the  French 
sum  :  to  the  sterhag  required. 

To  change  Sterling  into  French. 
Rule.  As  the  rate  of  exchange  :  is  to  1  crown  :  :   so  is  tho 
aterhng  sum  :  to  the  French  required. 

EXAMPLES. 
1.    How  many  crowns  must  be  paid  at  Paris,  to  receive  in 
London  ill 80  exchanged  at  4s.  6d.  per  crown? 

d.    c.        £ 
As  54  :  1  :  :  180  :  800. 
240 


ii 


64)43200(800  crowns. 
432 

^     2.  How  much  sterling  must  be  paid  in  London,  to  receive  in 
Paris  758  crowns,  exchanged  at  66d.  per  crown? 

Ans.  £176  :  17  :  4. 

3.  A  merchant  in  London  remits  £176  :  17  :  4,  to  his  corres- 
pondent  at  Paris;  what  is  the  value  in  French  crowns,  at  5bd. 
'^  „  0  Ans.  758. 
per  crown  i                                               .               . ,  i 

4.  Change  725  crowns,  17  sols,  7  demers,  at  54^d.  per  crown, 
into  sterling,  what  is  the  sum?  Ans.  £164  :  14  :  O^d.^h 

5.  Change  £164  :  14  :  0^  sterUng,  into  French  crowns,  ex- 
change at  54^d.  per  crown  ?       .  ^     ,     w    , ,     i     • 

Ans.  725  crowns,  17  sols,  7  yVV  demers. 

11.  SPAIN. 
They  keep   their   accounts  at  J^ladrid,  Cadiz   and  Seville,  in 
dollars,  rials,  and  maravedies,  and  exchange  by  the  piece  of  eight 
=4s.  6d.  at  par. 

Note.  34  maravedies  make  1  rial. 

8  rials. 1  piastre  or  piece  of  eight.  ^ 

10  rials 1  dollar.  | 

Kjle.  As  with  France.  ^' 

EX'aMPLES.  m9L*' 

6.  A  merchant  at  Cadiz  remits  to  London  2547  pieces  of  eighty 

at  56d.  per  piece,  how  much  sterling  is  the  sum  ? 

Ans.  £594  :  6. 


EXCHANGE.  Hf^ 

1.  How  many  pieces  of  eight,  at  56d.  each,  will  answer  a  hill 
of  £594  :  6,  sterling  ]  Ans.  2547. 

8.  If  I  pay  a  bill  here  of  £2500,  what  Spanish  money  may  1 
draw  my  bill  for  at  Madrid,  exchange  at  57^d.  per  piece  of  eighth 

Ans.  10434  pieces  of  eight,  6  rials,  8  mar.  || 

III.  ITALY. 

They  keep  their  accounts  at  Genoa  and  Leghoni,  in  livrcs, 
sols,  and  deniers,  and  exchange  by  the  piece  of  eight,  or  dollar 
=4s.  6d.  at  par. 

Note.     12  deniers  make  1  sol. 
20  3ols 1  livre. 

5  livres 1  piece  of  eight  at  Genoa. 

6  livres 1  piece  of  eight  at  Leghorn. 

N.  B.  The  exchange  at  Florence  is  by  ducatoons ;  the  exchange  at  Venice 
by  ducats. 

Note.      6  solidi  make  1  gross. 
24  gross 1  ducat 

Rule.     Same  as  before. 

9.  How  much  sterling  money  may  a  person  receive  in  London,  if  he 
pays  in  Genoa  976  dollars,  at  53d.  per  dollar  ?  Ans.  £215  .  10  .  S. 

10.  A  factor  has  sold  goods  at  Florence,  for  250  ducatoons,  at  54d.  each  ; 
what  IS  the  value  in  pounds  sterling  .'  Ans.  £5Q  .  5  .  0. 

11.  If  275  ducats,  at  4s.  5d  each,  be  remitted  from  Venice  to  London ; 
what  IS  the  value  in  pounds  sterling  .'  Ans.  £60  .14,7. 

12.  A  gentleman  travelling  would  exchange  £60  .  14  .  7,  sterling,  for 
Venice  ducats,  at  4s.  5d.  each  ;  how  many  must  he  receive  ? 

Ans.  275. 

IV.  PORTUGAL. 

They  keep  their  accounts  at  Oporto  and  Lisbon,  in  reas,  and 
exchange  by  the  milrea=6s.  8^d.  at  par. 

Note.     1000  reas  make  1  milrea. 
Rule.     The  same  as  with  France. 

EXAMPLES 

13.  A  gentleman  being  desirous  to  remit  to  his  correspondent  in  London 
2750  milreas,  exchange  at  6s.  5d.  per  milrea ;  how  much  sterling  will  he 
be  the  creditor  for  in  London  ?  Ans.  £882  .5.10. 

14.  A  merchmit  at  Oporto  remits  to  London  4366  milreas,  and  J  83  reas, 
at  5s.  5td.  ftsphang,^  pfr  milrea;  how  much  sterling  must  be  paid  in  Lon- 
don for  this  remittance  .'  Ans.  £1193  .  17  .  6|,  0375, 

15.  If  1  pay  a  bill  in  London  of  £1193  .  17  .  6|,  0375,  what  must  I  draw 
for  on  my  correspondent  in  Lisbon,  exchange  at  5s.  5gd.  per  milrea  ? 

Ans,  4366  milreas,  183  reas. 


^. 


IMAGE  EVALUATION 
TEST  TARGET  (MT-3) 


1.0 


I.I 


laiii  12.5 

1^    i;£    1112.0 


1.8 


1.25  1  1.4      1.6 

^ 

6"     

► 

V] 


V. 


^;. 


y^ 


7 


Photographic 

Sciences 

Corporation 


23  WEST  MAIN  STREET 

WEBSTER,  NY.  14580 

(716)  872-4503 


U.x 


.<> 


04 


BXCHANOB. 


V.  HOLLAND,  FLANDERS,  AND  GERMANY. 


They  keep  their  accounts  at  Antwerp  Amsterdam  Bru^^^^^^^ 
RoSam,  and  Hamburgh,  some  in  pounds,  f  ""-f^'^^^r^d 
as  in  England;  others  in  guilders,  ^^ivers  and  pennings ,  ana 
Txchange  lith  us  in  our  pound,  at  33s.  4d.  Flemish,  at  par.  • 

Note.    8  pennings  make J  gjoat- 

2  groats,  or  16  pennings. ...  1  stiver. 
2oftivev3 : 1  guilder  or  florin. 

ALSO, 

12  groats,  or  6  stivers  make.  .1  scheUing. 
20  schelUngs,  or  6  guilders. . .  1  pound. 

To  change  Flemish  into  Sterling. 
Rule.    As  the  given  rate :  is  to  one  pound  :  :  so  is  the  Flemish 
turn :  to  the  sterling  required. 

To  change  Sterling  into  Flemish. 
Rule.    As  £1  sterling :  is  to  the  given  rate : :  so  is  the  sterUng 
given :  to  the  Flemish  sought.  ' 

EXAMPLES. 

at  33s.  Gd.  Flemish  per  PO""d  ^terljn^.  many'guildevs  must 

18.  If  I  pay  in  London  £8.)2  .  12  .  6.  spelling,  n  J  ^         j^,,  per 

Idraw  for  at  Amsterdam.  -^^-^;/9^,,^^g^,t!'l3  st?^^^ 
pound  sterling  ?  j^^^aJ  if  l  nav  in  Amsterdam  8792  guild. 

^  19.  What  must  I  draw  for  at  London,  'f     "^^^  >^J^^'l^^'^,,,,^  .terling  ? 
13  stiv.  14i  pennings,  exchange  at  34  schel.  4i  groats  pe^r^po  ^^    ^^    ^  B 

To  convert  Bank  Money  into  Current,  and  the  contrary. 
Ki^^r.    ThA  Bank  Money  is  worth  more  than  the  Current. 
ThSer^:  ^"eeri^one'and  the  other  is  called  agio,  .nd  . 
generally  from  3  to  6  per  cent,  in  favour  of  the  Bank. 

To  change  Bank  into  Current  Money. 


Rule.    As  100  guilders  Banlc :  is  to  100  with  the  agio 
«>  is  the  Bank  given :  to  the  Current  requii--^ 


ed. 


EXCHAN6S. 


99 


To  chanffe  Currents  Money  into  Bank. 

Rule.  As  100  with  the  agio  is  added  :  is  to  100  Bank  :  :  so  is 
the  Current  money  given  :  to  the  Bank  required. 

20.  Change  794  guilders,  15  stivers,  Current  Money,  into  Bank 
florins  agio  4f  per  cent. 

Ans.  161  guilders,  8  stivers,  llif-f  pennings. 

21.  Change  761  guildei-s,  9  stivers  Bank,  into  Current  Money, 
agio  4f  per  cent. 

Ans.  794  guilders,  15  stivers,  ij\  pennings. 
VI.  IRELAND. 

22.  A  gentleman  remits  to  Ireland  £575  :  15,  sterling,  wluit 
will  he  receive  there,  the  exchange  being  at  10  per  cent? 

Ans.  £633  :  6  :  6. 

23.  What  must  be  paid  in  London  for  a  remittance  of  £633  : 
6  :  6,  Irish,  exchange  at  10  per  cent.  ?  Ans.  575  :  15. 

COMPARISON  OF  WEIGHTS  AND  MEASURES. 

EXAMPLES. 

.  If  50  Dutch  pence  be  worth  65  French  pence,  how  many 
Dutch  pence  are  equal  to  350  French  pence  ? 

Ans.  269Af . 

2.  If  12  yards  at  London  make  8  ells  at  Paris,  how  many  elb 
at  Paris  will  make  64  yards  at  London  ? 

Ans.  42y«y. 

3.  If  30  lb.  at  London  make  28  lb.  at  Amsterdam,  how  many 
lb.  at  London  will  be  equal  to  350  lb.  at  Amsterdam  ? 

«  Ans.  375. 

4.  If  95  lb.  Flemish  make  100  lb.  English,  how  many  lb.  En- 
glish are  equal  to  275  lb.  Flemish. 

Ans.  289f f. 
CONJOINED  PROPORTION, 

Is  v4ien  the  coin,  weights,  or  measures  of  stjveral  countries  are 
compared  in  the  same  question ;  or,  it  is  linking  together  a  varie- 
ty of  proBprtions. 

Whenlfc  is  required  to  fii 
weig)^  or  measure,  mentioned 
given  quantity  of  the  last. 


how  many  of  the  first  sort  of  coin, 
in  the  question,  are  equal  to 


96 


PROPORTION. 


Rule.  Place  the  nundfers  alternately,  beginning  at  the  left 
hand,  and  let  &e  last  number  stand  on  the  left  hand ;  then  multi- 
ply the  first  row  continually  for  a  dividend,  and  the  second  for 
a  divisor. 

Proof.  By  as  many  single  Rules  of  Three  as  the  question 
requires. 

EXAMPLES. 


1.  If  20  lb.  at  London  make  23  lb.  at  Antwerp,  and  155  lb. 
at  Antwerp  make  180  lb.  at  Leghorn,  how  many  lb.  at  London 
are  equal  to  '72  lb.  at  Leghorn  ? 


20X155X'72=223200 
23X180=4140)223200(53|H- 


2.  If  12  lb.  at  London  make  10  lb.  at  Amsterdam,  and  100  lb. 

:^t  Amsterdam  120  lb.   at  Thoulouse,  how  many  lb.  at  London 

are  equal  to  40lb.  at  Thoulouse  ? 

*     ^  Ans.  40  lb. 


Left. 

RigEt. 

20 

23 

155 

180 

72 

"  K'U. 


3.  If  140  braces  at  Venice  are  equal  to  156  braces  at  Leghorn, 
and  7  braces  at  Leghorn  equal  to  4  ells  English,  how  many  bra- 
ces at  Venice  are  equal  to  16  ells  English? 

Ans.  26^.  ^ 

4.  If  40  lb.  at  London  make  36  lb.  at  Amsterdam,  and  90  tb. 
at  Amsterdam  make  116  at  Dantzick,  how  many  lb.  at  London 
are  equal  to  130  lb.  at  Dantzick  ? 

Ans.  112,VtV- 

When  it  is  required  to  find  how  many  of  the  last  sort  of  ^n, 
sight,  or  measure,  mentioned  in   the   question,  are  equal  to  a 
quantity  of  the  first.  » 

Rule.  Place  the  numbers  alternately,  beginning  H  the  left 
hand,  and  let  the  last  number  stand  on  the  right  hand ;  tliefe  mul- 
tiply the  first  row  for  a  divisor,  and  the  second  for  a  dividend. 


weig 


PR06HESSI0N.  #t 

EXAMPLES.      f 

6.  If  12  lb.  at  London  make  10  lb.  at  Amsterdam,  and  100  lb. 
at  Amsterdam  120  lb.  at  Thoulouse,  how  many  lb.  at  Thoulouse 
are  equal  to  40  lb.  at  London  ?  Ans.  40  lb. 

6.  If  40  lb.  at  London  make  36  lb.  at  Amsterdam,  and  90  lb. 
at  Amsterdam  116  lb.  at  Dantzick,  how  many  lb.  at  Dantzick  are 
equal  to  122  lb.  at  London?  Am.  14mj|. 

PROGRESSION 

CONSISTS  OF  TWO  PARTS 

ARITHMETICAL  AND  GEOMETRICAL. 

ARITHMETICAL  PROGRESSION 

Is  when  a  rank  of  numbers  increase  or  decrease  regularly  by  the 
continual  adding  or  subtracting  of  equal  numbers ;  as  1,  2,  3,  4, 
6,  6,  are  in  Arithmetical  Progression  by  the  co;>Unual  increasing 
or  adding  of  one;  11,  9,  7,  5,  3,  1,  by  the  continual  decreasing 
or  subtracting  of  two. 

Note.  When  any  even  nurnVar  of  terms  differ  i  .y  Arithme- 
tical Progression,  the  sum  of  the  two  extremes  will  be  equal 
to  the  two  middle  numbers,  or  any  two  means  equally  distant 
from  the  extremes;  as  2,  4,  6,  8,  10,  12,  where  6+8,  the  two 
middle  numbers,  are=12+2,  the  two  extremes,  and=10-|-4  the 
two  means =14. 

When  the  number  of  terms  are  odd,  the  double  of  the  middle 
term  will  be  equal  to  the  two  extremes;  or  of  any  two  means 
equally  distant  from  the  middle  term ;  as  1,  2,  3,  4,  6,  where  the 
double  number  of  3=5+1=2+4=6. 

In  Arithmetical  Progression  five  things  are  to  be  observed,  viz. 

1.  The  first  term;  better  expressed  thus,  F. 

2.  The  last  term, L. 

•i  3.  The  number  of  terms, N. 

J  1.,  4    The  equal  difference,  . . .' D 

5.  The  sum  of  all  terms, S. 

Any  three^f  which  being  given,  the  other  two  may  be  found. 
The  nrsi,  «i©ond,  and  third  terms  given,  to  find  the' fifth. 

Rule.  Multiply  the  sum  of  the  two  extremes  by  half  the 
number  of  %rms,  or  multiply  half  the  sum  of  the  two  extremes 


06 


PBOORE88ION. 


by  the  whole  number  of  terms,  the  product  is  the  total  of  fdl  the 
terms :  or  thus, 


I.      F  L  N  are  given  to  find  S. 

N 

F+Lx— =S. 

2 

EXAMPLES. 


i 


k^. 


1.  How  many  strokes  does  the  hammer  of  a  clock  strike  in  12 
hours  ? 

12  +  1  =  13,  then  13X6='78. 

2.  A  man  bought  17  yards  of  cloth,  and  gave  for  the  firat  yard 
2s.  and  for  the  last  10s.  what  did  the  17  yards  amount  to? 

Ans.  £5  .  2. 

3.  If  100  eggs  were  placed  in  a  right  line,  exactly  a  yard  as- 
under from  one  another,  and  the  first  a  yard  from  a  basket,  what 
length  of  ground  does  that  man  go  who  gathers  up  these  100  eggs 
smgiy,  and  returns  with  every  egg  to  the  basket  to  put  it  in  ? 

Ans.  5  miles,  1300  yards. 

,%€(  first,  second,  and  third  terms  given,  to  find  the  fourth. 

Rule.  From  the  second  subtract  the  first,  the  remainder  divi- 
ded by  the  third  less  one,  gives  the  fourth :  or  thus 

F  L  N  are  given  to  find  D. 
L — F 
=D. 


N— 1 


EXAMPLES. 


4.  A  man  had  eight  sons,  the  youngest  was  4  years  old,  and 
the  eldest  32,  they  increase  in  Arithmetical  Progress!^  what 
was  the  common  difference  of  their  ages  ?  ^      ^JW.  4. 

32—4=28,  then  28-r  8 = 1 +4  common  dii||enc^.       * 

6.  A  man  is  to  travel  from  London  i 
days,  and  to  go  but  3  miles  the  fii-st  day. 


mcreasin 
an  equal  excess,  so  that  the  last  day's  journey 


of  all  the 


•ike  in  12 


first  yard 

)9 

1  • 
£5.2. 

yard  as- 
iket,  what 

100  eggs 

in? 
>  yards. 

irth. 

ader  divi- 

3  old,  and 
iitm,  what 
Aim,  4. 


ce. 


laee  in  12 

»jrda3|% 

58  miles, 


PROGRESSION. 

what  is  the  daily  increase,  and  how  many  miles  distant  is  that 
place  from  London  ?  Am.  5  daily  increase. 

Therefore,  as  three  miles  is  the  first  day's  journey, 

3-f-6=8  the  second  day.  • 
8+5  =  13  the  third  day,  &c. 
The  whole  distance  is  366  miles. 

The  first,  second,  and  fourth  terms  given,  to  find  the  third. 

Rule.  From  the  second  subtract  the  first,  the  remainder  divide 
by  the  fourth,  and  to  the  quotient  add  1,  gives  the  third ;  or  thus, 

III.         F  L  D  are  given  to  find  N. 
.       L^F 

— +1=N. 


D 


EXAMPLES. 


6.  A  person  travelling  into  the  country,  went  3  miles  the  first 
day,  and  increased  every  day  5  miles,  till  at  last  he  went  68  miles 
in  one  day ;  how  many  days  did"  he  travel  ?  An%,  12. 

68—3=55-7-5  =  11  +  1  =  12  the  number  of  days. 

7.  A  man  being  asked  how  many  sons  he  had,  said,  that  the 
youngest  was  4  years  old,  and  the  oldest  32 ;  and  that  he  increas- 
ed one  in  his  family  every  4  years,  how  many  had  he  ? 

Ans.  8. 
The  second,  third,  and  fourth  terms  given  to  find  the  first. 

Rule.  Multif)ly  the  fourth  by  the  third  made  less  by  one,  the 
product  subtracted  from  the  second  gives  the  first :  or  thus, 

IV.        L  N  D  are  given  to  find  F. 


■  ■^W*4, 


L— DxN— 1=F. 


EXAMPLES. 


8.  A  man  in  10  days  went  from  London  to  a  certain  town  in 


the  countryi  every  day's  journey  increasing  the  former  by  4,  and 

i  Ans.  10  miles. 

4X10—1=36,  then  46—36=10,  the  firat  day's  journey. 

12 


100 


PROGRESSION. 


9.  A  man  taues  out  of  his  pocket  at  8  several  times,  so  many 
diflferent  numbers  of  shillings,  every  one  exceeding  the  former 
by  6,  the  last  at  40 ;  what  was  the  first  ?  ^ns.  4. 

The  fourth,  third,  and  fifth  given,  to  find  the  first. 

EuLE.  Divide  the  fifth  by  the  third,  and  from  the  quotient 
subtract  half  the  product  of  the  fourth  multiplied  by  the  third 
less  1  gives  the  first :  or  thus,  ^ 

V.    N  D  S  are  given  to  find  F. 


SDXN— 1 


— F. 


N2 


EXAMPLES. 
10   A  man  is  to  receive  £360  at  12  several  payments,  each  to 
exceed  the  former  by  £4,  and  is  wilHng  to  bestow  the  first  pay- 
ment on  any  one  that  can  tell  him  what  it  is.     What  will  that 
person  ha.ve  for  his  pains  ?  ^^*-  *S- 

4X12—1 

360-12=30,  then  30 =£8  the  first  payment. 

2 
The  first,  third,  and  fourth,  given  to  find  the  second. 
Rule.  Subtract  the  fourth  from  the  product  of  the  third,  mul- 
tiplied by  the  fourth,  that  remainder  added  to  the  first  gives  the 
second :  or  thus, 

F  N  D  are  given  to  find  L. 
\  ND— D+F=L. 

EXAMPLES. 
11    What  is  the  last  number  of  an  Arithmetical  Progression, 
beginning  at  6,  and  continuing  by  the  increase  of  8  to  20  places? 
°        ®  Ans.  168. 


20x8—8=152,  then  152+6  =  158,  the  last  number^ 
GEOMETRICAL  PROGRESSION 

«       .-.         .  _? J- ^^:«/.    y^f   n«ir    ran\z   nf    TtllTTlbt^Ra    bv  SOlQft 

is  tne  increasing  ui  ucvicarsmg  ui  «t.j  -^^ ,.""': "    v  •  '"' 

common  ratio;  that  is,  by  the  continual  multiphcation  or  division 
of  some  equal  number:  as  2,  4,  8,  10,  increase  by  the  mum^lwr 
2,  and  16,  8,  4,  2,  decrease  by  the  divisor  2. 


\^ 


PROORB88ION. 


101 


Note.   When  any  number  of  terms  is  continued  in  Geome- 
trical Progression,  the  product  of  the  two  extremes  will  bo  equal 
to  any  two  means,  equally  distant  from  the  extremes:  as  2,  4,  8 
16,  32,  64,  where  64X2  are=4X32,  and  8X16=128. 

When  tlie  number  pi  the  terras  are  odd,  the  middle  term  mulU- 
phed  mto  itself  will  be  equal  to  the  two  extremes,  or  any  two 
means  equally  distant  from  it,  as  2,  4,  8,  16,  32,  where  2X32  = 
4X16  =  8X8=64. 

.  In  Geometrical  Progression  the  same  5  things  are  to  be  obser- 
ved as  are  in  Arithmetical,  viz. 

1.  The  first  term. 

2.  The  last  term.  * 

3.  The  number  of  terms. 

4.  The  equal  difference  or  ratio. 
6.  The  sum  of  all  the  terms. 

Note.  As  the  last  term  in  a  long  series  of  numbers  is  very 
tedious  to  come  at,  by  continual  multiplication ;  therefore,  for  the 
reader  finding  it  out,  there  is  a  series  of  numbers  made*  use  of 
in  Anthmetical  Proportion,  called  indices,  beginning  with  an 
unit,  whose  common  difference  is  one ;  whatever  number  of  in- 
dices you  make  use  of,  set  as  many  numbei-s  (in  such  Geomet- 
rical I  roportion,  as  is  given  in  the  question)  under  them. 

^  1,  2,  3,    4,    5,    6,  Indices. 

2,  4,  8,  16,  32,  64,  Numbers  in  Geometrical  Proportion. 

But  if  the  fii-st  term  in  Geometrical  Proportion  be  different 
ti-om  the  ratio,  the  indices  must  begin  with  a  cipher. 

As  ^'  ^'  2,  3,    4,    5,    6,  Indices. 

1,  2,  4,  8,  16,  32,  64,  Numbers  in  Geometrical  Proportion. 

When  the  Indices  begin  with  a  cipher,  the  sum  of  the  indices 
made  choice  of  must  always  be  one  less  than  the  number  of  terms 
given  m  the  question;  for  1  in  the  indices  is  over  the  second 
term,  and  2  over  the  third,  &c. 

Add  any  two  of  the  indices  together,  and  that  sum  will  affree 
with  the  product  of  their  respective  terms. 

Aft  in   tha  firaf  taVKl/^  nf  l^Ji: ct    I       ^  t, 

— —  —    -...,   ,,,,.v   ittvit:   vri     xiiuiuca   ;; -J""     0=         7 

Geometri    '  '^ 


Proportion 


•  •  •  •  • 


4X32=128 


Then  the  second  2+4=     6 

4X16=  64 
13 


f  I 


102 


PROOHESSION. 


In  any  Geometrical  Progression  proceeding  from  unity,  the 
ratio  being  known,  to  find  any  remote  term,  without  producmg 
all  the  intermediate  terms. 

Rule.  Find  what  figures  of  the  indices  added  together  would 
eive  the  exponent  of  the  term  wanted:  then  multiply  the  num- 
lerB  standing  under  such  exponents  into  each  other,  and  it  will 
give  the  t«rm  required. 

Note.  When  the  exponent  1  stands  over  the  second  tem^ 
the  number  of  exponents  must  be  one  less  than  the  number  of 
terms. 

*      EXAMPLES. 

1.  A  man  agrees  for  12  peaches,  to  pay  only  the  price  of  the 
last,  reckoning  a  farthing  for  the  fii-st,  and  a  halfpenny  for  the 
second,  &c.  doubling  the  price  to  the  last;  what  must  he  give 
for  them?  ^n..  £2  .  2  .  8. 


k: 


0,  1,  2,  3,    4,  Exponents 

1,  2,  4,  8,  16,  No.  of  terms. 


16=4 
16  =  4 

256  =  8 
8=3 


For  4+4+3=11,  No.  of  terms  less  1 


4)2048=11  No.  of  far." 

12)512 

210)412  .  8 


£2.2.8 

2.  A  comitry  gentleman  going  to  a  fair  to  buy  some  oxen, 
meek  with  a  person  who  had  23 ;  he  demanded  the  pnce  of  them, 
^d  wJanswered  £16  a  piece;  the  gentleman  bids  £15  a  p^e 
«d  Twould  buy  all ;  the'other  tells  him  it  could  not  be^l^ken 
but  if  he  would  iive  what  the  last  ox  would^come  to,  at  a  farming 
for  the  first,  and  doublinc.  it  to  the  last,  he  should  hav^all.  ^  What 
was  the  price  of  the  oxen  %  ^''''  ^-"^     ''% 

In  any  Geometrical  Progression  not  Proceeding  fro«a  unity, 
the  ratio  being  given,  to  find  any  remote  term,  without  produ- 
cing all  the  intermediate  terms. 


PBoaRBisioir. 


198 


Rule.  Proceed  as  in  the  last,  only  observe,  that  every  product 
must  be  divided  by  the  fii-st  term. 

EXAMPLES. 

3.  A  sum  of  money  is  to  be  divided  amon^r  eight  persons,  the 
first  to  have  £20,  the  next  £60,  and  so  in  triple  proportion  ;  what 
will  the  hist  have  ?  Ans.  £43U0. 


640X640 


14580X60 


0,    1,      2,      3, 
20,  60,  180,  540, k=14580,  then =43740 

20  20 

34-3+1=7,  one  less  than  the  number  of  terms. 

4.  A  gentleman  dying,  left  nine  sons,  to  whom  and  to  his  exe- 
cutors he  bequeathed  his  estate  in  the  manner  following :  To  his 
executors  £50,  his  youngest  son  was  to  have  as  much  more  as 
the  executors,  and  each  son  to  exceed  the  next  younger  by  as 
much  more ;  what  was  the  eldest  son's  proportion  ? 

Ans.  £2560Q. 

The  firet  term,  ratio,  and  number  of  terms  given,  to  find  the 
sum  of  all  the  terms. 

Rule.  Find  the  last  terra  as  before,  then  subtract  the  first 
from  It,  and  divide  the  remainder  by  the  ratio,  less  1 ;  to  the  quo- 
tient  of  which  add  the  P^reater,  gives  the  sum  required. 


EXAMPLES. 


5.  A  servant  skilled  in  numbers,  agreed  wit^  a  gentleman  to 
serve  him  twelve  months,  provided  he  would  give  him  a  farthinjr 
:f  .^'  T^^>  "month's  service,  a  penny  for  the  second,  and  4d.  for 
tne  third,  &c.,  what  did  his  wages  amount  to  ? 

Ans.  £5825  .  8  .  6^. 

256X256=65536,  then  65536X64=4194304 
0»  h    2,    3,      4,  4194304—1 

l'A^.^^;?^^»         ^-r =1398101,  then 

4+4+3=11  No.  of  terms  less  1,  4—1 

1398101+4194304=5592405  farthings. 

I  tu'^'  ^  ^^*"  uoti^t  a  horse,  and  by  agreement  was  to  give  a  far- 
thing for  the  first  nail,  three  for  the  second,  &c.,  there  were  four 
shoes,  and  in  each  shoe  8  nails ;  what  was  the  worth  of  the  horse  ? 
^,  Ans.  £965114681693  .  13  .  4. 


/ 


/i 


tot 


PERMUTATION. 


1  A  certain  pereon  married  his  daughter  on  New-years  da.y, 
and'eave  her  husband  Is.  towards  her  marriage  portion,  proniis- 
ing  to  double  it  on  the  first  day  of  every  month  for  1  year ;  what 
waa  her  portion?  ^n5.  £204  .  15. 

8  A  laceman,  well  versed  in  numbers,  agreed  with  a  gentle- 
man  to  sell  him  22  yards  of  rich  gold  brocaded  lace,  for  2  pms 
the  fii-st  yard,  6  pins  the  second,  &c.,  in  triple  proportion ;  1 
desire  to  know  what  he  sold  the  lace  for,  if  the  pins  were  valued 
at  100  for  a  farthing;  also  what  the  laceman  got  or  lost  by  the 
«ae  thereof,  supposing  '^jj,- ^^^''™J",f  ,^^6^^^^^^  0  .  9. 

Gain  £326732  .0.9. 

PERMUTATION 

Is  the  changing  or  varying  of  the  order  of  things. 

Rule.  Multiply  all  the  given  terms  one  into  another,  and  the 
last  product  will  be  the  number  of  changes  required. 

EXAMPLES. 

1  How  many  changes  may  be  rung  upon  12  bells;  and  how 
long  would  they  be  ringing  but  once  over,  supposing  JO  changes 
might  be  rung  in  2  minutes,  and  the  year  to  contam  365  days,  6 
hours?         '"^  ,;^-.,, 

1X2X3X4X5>C6X^  X  8  X  9  X  10  X  H  X  12  =  479001600 
changes,  which  -^  10=47900160  minutes ;  and,  if  reduced,  is=91 
years,  3  weeks,  6  days,  6  hours. 

2  A  young  scholar  coming  to  town  for  the  convenience  of  a 

good  library,  demands  of  a  gentleman  with  whom  he  lodged, 

what  his  diet  would  cost  for  a  year,  who  told  him  £10  but  the 

scholar  not  being  certain  what  time  he  should  stay,  asked  him 

what  he  must  give  him  for  so  long  as  he  should  place  his  family, 

(consisting  of  6  persons   besides   himself)  m  different  J?osition^ 

^ .!„„  „*   ,K««««.   *\^a  n-AntlAman   thinkinfif   it  woul*  not  be 

every   uay   «»<   m'"'^-^^  j    ^"^-   & -  =?       „ti    j.  !•         j;,i 

long,  tells  him  £5,  to  which  the  scholar  agrees.     What  time  did 

the  scholar  stay  with  the  gentleman?  ^ 

Ans,  6040  days. 


105 


fdi^ 


THE 


t.^ 


TUTOR'S  ASSISTANT. 


PART  II. 


VULGAR  FRACTIONS. 

A  FRACTION  is  a  part  or  parts  of  an  unit,  and  written  with  two 
figures,  with  a  Une  between  them,  as  ^,  f ,  f ,  &c. 

The  figure  above  the  Une  is  called  the  numerator,  and  the  un- 
der one  the  denominator ;  which  shows  how  many  parts  the 
unit  is  divided  into :  and  the  numerator  shows  how  many  of 
those  parts  are  meant  by  the  fraction. 

There  are  four  sorts  of   vulgar  fractions:  proper,  improper 
compound,  and  mixed,  viz.  ' 

11.  A  PROPER  FRACTION  is  whcu  the  numerator  is  less   than 
the  d^ominator,  as  |,  |,  J,  j-f,  |ii  &c. 

"i 

2.  An  IMPROPER  FRACTION  is  when  the  numerator  is  ^^qual 
to,  or  greater  than  the  denominator,  as  f ,  f ,  ||,  iii,  &c. 

^    3.  4^  COMPOUND  FRACTION  IS  the  fraction  of  a  fraction,  and 
tuowuwy  the  word  of,  as  ^  of  f  of  f  of  j\  of  y'j,  &c. 

4.  A  MIXED  NUMBER,  or  FRACTION,  ia  composed  of  a  whbla 
aumber  and  fraction,  as  8|.  17^,  8J|,  &c. 


106 


REDUCTION  OF  VULGAR  FRACTIONS. 


REDUCTION  OF  VULGAR  FRACTIONS. 

1.  To  reduce  fractions  to  a  common  denominator. 

Rule.  Multiply  each  numerator  into  all  the  denominators, 
except  its  own,  for  a  numerator;  and  all  the  denominators,  for 
a  common  denominator.     Or, 

2.  Multiply  the  common  denominator  by  the  several  given 
numerators,  separately,  and  divide  their  product  by  the  several 
denominators,  the  quotients  will  be  the  new  numerators. 

EXAMPLES. 

1.  Reduce  |  and  4  to  a  common  denominator. 

Facit,  If  and  |f 

Ist  num.         2d  num. 

2X1 -U     4X4  =  16,  then  4X'7=28  den.=if  and  ff. 

2.  Reduce  i.  L  and  4,  to  a  common  denominator. 

Facit,  II,  tf ,  il 

3.  Reduce  |,  f ,  y%,  and  4,  to  a  common  denominator. 

Pn(^\f  2-9  4  0  aaAii  a.jOLi6   am. 

rdUt,    3  3flo^j    3360»    3360)    3360* 

4.  Reduce  y^i  h  h  ^^^  h^^  common  denominator. 

Fa<5it,  \nh  iWo,  M^)  tVA- 

5.  Reduce  i,  |,  4,  and  i,  to  a  common  denominator. 

6.  Reduce  f ,  |,  |,  and  f ,  to  a  common  denominator. 

Fnpit    -TiUL    iiAli    -i'-M^    J^^l^4 
racii,  2  If  o»  at  e  0)  2ioir»  2  if  IT* 

2.  To  reduce  a  vulgar  fraction  to  its  lowest  terms. 

Rule.  Find  a  common  measure  by  dividing  the  lower  term 
by  the  upper,  and  that  divisor  by  the  remainder  following,  till 
nothing  remain:  the  last  divisor  is  the  common  measure;  then 
divide  both  parts  of  the  fraction  by  the  common  measure,  and 
the  quotient  will  give  the  fraction  required. 

Note.  If  the  common  measure  happens  to  be  one,  the  fraction 
is  already  in  its  lowest  term :  and  when  a  fraction  hath  ciphers  at 
the  right  hand,  it  may  be  abbreviated  by  cutting  them  off,  as  f  1^. 

EXAMPLES. 

7.  Reduce  44  to  its  lowest  terms.  ^ 

24^32(1 
24 


Com.  measure,       8)24(3  Facit. 


)NS. 


lenominators, 
minators,  for 

leveral  given 
'  the  several 
rs. 


^f  and  If 


and  if. 


aa  11  Ai. 

B4)   04'    64' 

tor. 

<L16     a.881 
36  0)    3  3  0  0* 

itor. 

JdL.     JL4JL. 
B  8ff»    16  85^* 

560     105 
'    84  0»    »♦«• 

or. 


e  lower  term 
following,  till 
leasure;  then 
measure,  and 

3,  the  fraction 
ath  ciphers  at 
a  off,  as  |tf 


KEDUCTION   OP  VULGAR   FRACTIONS. 


wt 


k 


Facit,  ^«L. 

Facit,  VV't- 

Facit,  ^, 

Facit,  If. 

Facit,  f . 


8.  Reduce  f^^  to  its  lowest  terms. 

9.  Reduce  f  f  |  to  its  lowest  terms. 

10.  Reduce  iff  to  its  lowest  terms. 

11.  Reduce  |f  ^  to  its  lowest  terms.   ^ 

12.  Reduce  f iff  to  its  lowest  terms. 

3.  To  reduce  a  mixed  number  to  an  improper  fraction. 

Rule.  Multiply  the  whole  number  by  the  denominator  of 
the  fraction,  and  to  the  product  add  the  numerator  for  a  new 
numerator,  which  place  over  the  denominator. 

Note.  To  express  a  whole  number  fraction-ways  set  1  for  the 
denominator  given. 

EXAMPLES. 

13.  Reduce  18-^  to  an  improper  fraction.  Facit,  i|A, 


11^7+3  =  129  new  numerator=if  a. 
14.  Reduce  56if  to  an  improper  fraction. 
16.  Reduce  183/y  to  an  improper  fraction. 
16.  Reduce  13f  to  an  improper  fraction. 
llT.  Reduce  2*71  to  an  improper  fraction. 

18.  Reduce  514/^  to  an  improper  fraction. 
4.  To  reduce  an  improper  fraction  to  its  proper  terms. 
Rule.  Divide  the  upper  term  by  the  lower. 

EXAMPLES. 

19.  Reduce  if  ^  to  its  proper  terms. 

129-7-7=18f 

20.  Reduce  i||i  to  its  proper  terms. 

21.  Reduce  ^|f^  to  its  proper  terms. 

22.  Reduce  ^  to  its  proper  terms. 

23.  Reduce  a^f  ^  to  its  proper  terms. 

24.  Reduce  -^f  f  ^  to  its  proper  terms. 


Facit,  i?-Ai. 


22 


Facit,  5811. 

Facit,  V- 

Facit,  ^s.. 

Facit,  iif  A. 


Facit,  18f 


Facit,  66|f . 
Facit,  183^. 

Facit,  13f. 

Facit,  2Yf . 
Facit,  514^^. 


6.  To  reduce  a  compound  fraction  to  a  sinffle  one. 

Rule.    Multiply   all    the    numerators  for  a  new  numerator, 
and  all  the  denominators  for  a  new  denominator. 
Reduce  the  new  fraction  to  its  lowest  terms  by  Rule  2. 


108 


KBDUCTION    OP   VULGAR    FRACTIONS. 

EXAMPLES. 


25.  Reduce  f  of  |  of  |  to  a  single  fraction. 

2X3X5=  30 
Pa(>jt  — reduced  to  the  lowest  term=i. 

'  3X5X8  =  120 

26.  Reduce  f  of  4  of  \^  to  a  single  fraction. 

27.  Reduce  U  of  If  of  |i  to  a  single  fraction. 

X"  ttVyl  L,    4  8  12 2  a  2 

28.  Reduce  |  of  |  of  -i?^  to  a  single  fraction. 

Fipil    135.  =  JL 

29.  Reduce  |  of  f  of  |  to  a  single  fraction. 


30.  Reduce  f  of  M^  to  *<>  »  »^»g^^  fraction. 


Fqpit    -8JL  —  J*- 


.6.  To  reduce  fractions  of  one  denomination,  to  the  fracti^Qn  of 
nnother,  but  greater,  retaining  the  same  value. 

Rule.  Reduce  the  given  fraction  to  a  compound  one,  by  cora- 
parino-  it  with  all  the  denominations  between  it  and  that  denomi- 
•    nation  which  you  would  reduce  it  to;  then  reduce  that  compound 
fraction  to  a  single  one. 

EXAMPLES.  # 

31.  Reduce  i  of  a  penny  to  the  fraction  of  a  pound. 

Facit,  i  of  y'a  of  2\'-^T9TtV' 

32.  Reduce  i  of  a  penny  to  the  fraction  of  a  pound. 

Facit,  ^^y. 

33.  Reduce  |  of  a  dwt.  to  the  fraction  of  a  lb.  troy. 

Facit,  ysU' 

34.  Reduce  ^  of  a  lb.  avoirdupois  to  the  fraction  of  a  cwt. 

Facit,  Tf\'f. 

1.  To  reduce  fractions  of  one  denomination  to  the  fraction  oF 
another,  but  less,  retaining  the  same  value. 

Rule.  Multiply  the  numerator  by  the  parts  contained  in  the 
several  denominations  between  it,  and  that  you  would  reduce  it 
to,  for  a  new  numerator,  and  place  it  over  the  given  denominator. 


BEDVCTION   OP   VULGAR  PHACTI0N8. 


109 


EXAMPLES. 

35.  Reduce  r^\j^  of  a  pound  to  the  fraction  of  a  penny. 

Facit,f 
7X20X12=1680  ^U  reduced  to  its  lowest  term=f 

36.  Reduce  ^^^  of  a  pound  to  the  fraction  of  a  penny. 

oT    r>   1  A       !•  Facit,  ^. 

d7   Keduce  ^a^iro  of  a  pound  troy,  to  the  fraction  of  a  penny- 
weight. 1?    •!    4   "^ 
oo    r»  J          M      i>                  ,                                    Facit,  4.* 

38.  Reduce  .^f  y  of  a  cwt.  to  the  fraction  of  a  lb. 

Facit,  f  . 

8.  To  reduce  fractions  of  one  denomination  to  anothor  of  the 
same  value,  havmg  a  numerator  given  of  the  required  fraction. 

Rule.  As  the  numerator  of  the  given  fraction  :  is  to  its  deno- 
mmator  :  :  so  is  the  numerator  of  the  intended  fraction  :  to  its 
denommator. 

EXAMPLES.       * 

39.  Reduce  f  to  a  fraction  of  the  same  value,  whose  numera- 
tor shall  be  12.  As  2  :  3  : :  12  :  18.  Facit,  j-a 

40.  Reduce  4  to  a  fraction  of  the  same  value,  whose  num'era- 
tor  shall  be  25.  p^^^jj^  4. 

41  Reduce  4  to  a  fra<5tion  of  the  same  value,  whose  numera- 
tor  shall  be  47.  4Y 

Facit, 

65|. 
9.  To  reduce  fractions  of  one  denbmination  to  another  of  the 
same  value,  having  the  denominator  given  of  thf.  fractions  re- 
quired. 

Rule.  As  the  denominator  of  the  given  fraction  :  is  to  its 
numerator  :  :  so  is  the  denominator  of  the  intended  fraction  :  to 
Its  numerator. 

EXAMPLES. 

#.  Reduce  f  to  a  fraction  of  the  same  value,  whose  denomi- 
nator shall  be  18.  As  3  :  2  :  :  18  :  12.  Facit,  |f . 

43.  Reduce  4  to  a  fraction  of  the  same  value,  whose  d'enomi- 
tor  shall  be  35.  Facit  M, 

44.  Reduce  4  to  a  fraction  of  the  same  value,  whose  denomi- 
nator shall  be  65|.  47 

Facit, 

65f 


110 


WEBDUCTION   aF   VULGAR   FRACTIONS. 


10.  To  reduce  a  mixed  fraction  to  a  single  one. 

Rule.  When  the  numerator  is  the  integral  part,  multiply  it 
by  the  denominator  of  the  fractional  part,  adding  m  the  numerator 
of  the  fractional  part  for  a  new  numerator ;  then  multiply  the  de- 
nominator of  the  fraction  by  the  denominator  of  the  fractional 
part  for  a  new  denominator. 

EXAMPLES.   . 

45.  Reduce — to  a  simple  fraction.  Facit,  |J^f — 4f. 

48 

3  6  X  3 + 2  =  1 1 0  numerator. 

48X3       =144  denominator.  ^ 

234 

46.  Reduce— to  a  simple  fraction.  Facit,  iff =1^3 • 

38 
When  the  denominator  is  the  integral  part,  multiply  it  by  the 
denominator  of  the  fractional  part,  adding  in  the  numerator  of 
the  fractional  part  for  a  new  denominator;  then  multiply^  the 
numerator  of  the  fraction  by  the  denominator  of  the  fractional 
pai-t  for  a  new  numerator. 

EXAMPLES. 

47..  Reduce— to  a  simple  fraction.  Facit,  Iff =4- 
65f 
19  .  _ 

48.  Reduce — to  a  simple  fraction.  Facit,  1V3— ^• 

11.   To  find  the  proper  quantity  of  a  fraction  in  the  known 
parts  of  an  integer. 

Rule.  Multiply  the  numerator  by  the  common  parts  of  the 
integer,  and  divide  by  the  denominator. 

EXAMPLES. 

49.  Reduce  |  of  a  pound  sterling  to  ita  proper  quantity. 
43X20=60-^4  =  153.  Facit,  16s. 

50    Reduce  ^  of  a  shilling  to  its  proper  quantity. 

Facit,  4d.  3i  qrs. 

61    Reduce  4  of  a  pound  avoirdupois  to  its  proper  quantity, 

Facit,  9  oz.  2^  dr. 

52.  Reduce  1  of  a  cwt.  to  its  proper  quantity. 

Facit,  3  qi-s.  3  lb.  1  oz.  12^  dr. 


Itiply  it 

merator 

the  de- 

•actional 


=  -8JL. 

133* 

t  by  the 
rator  of 
iply  the 
ractional 


9  known 
s  of  the 


y- 

it,  15s. 

3 1  qrs. 
mtity, 
2f  dr. 

12^  dr. 


liBtftCTlON   OP  VUtGA^fHACTIONS. 


iir 


63.  Reduce  f  of  a  pound  troy  to  its  proper  quantity. 

^ .    ^   .       ,    ^       „  „  Facit,  1  oz.  4  dwts. 

64.  Keduce  f  of*an  dl  English  to  its  proper  quantity. 

•rir   T>  J       *    ^      ^  ^»c'*»  2  qrs.  3^  nails. 

65.  Keduce  f  of  a  miJe  to  its  proper  quantity. 

^-   ^  ,  .  Facit,  6  fur.  16  poles. 

66.  Keduce  f  of  an  acre  to  its  proper  quantity. 

Facit,  2  roods,  20  poles. 
5/.  Keduce  f  of  a  hogshead  of  wine  to  its  proper  quantity. 

Ko   T>  J  1.  Facit,  64  gallons. 

68.  Keduce  |  of  a  barrel  of  beer  to  its  proper  quantity. 

^  Facit,  12  gallons. 

69.  Keduce  /^  of  a  chaldron  of  coals  to  its  proper  quantity. 

- .    _,   -  ^  Facit,  15  bushels. 

60.  Keduce  |  of  a  month  to  its  proper  time. 

Facit,  2  weeks,  2  days,  19  hours,  12  minutes: 
12.  To  reduce  any  given  quantity  to  the  fraction  of  any  greater 
denomination,  retaining  the  same  value. 

Rule.  Reduce  the  given  quantity  to  the  lowest  term  men- 
tioned for  a  numerator,  under  which  set  the  integral  part  reduced 
to  the  same  term,  for  a  denominator,  and  it  will  give  the  fraction 
required. 

EXAMPLES. 

61.  Reduce  ISs.  to  the  fraction  of  a  pound  sterling. 

^  ,  Facit,  if =|£. 

62.  Reduce  4.  3}  qrs.  to  the  fraction  of  a  shilling. 

63.  Reduce  9  oz.  2f  dr.  to  the  fraction  of  a  pound  avoirdupois. 

.  Facit,  4. 

64.  Reduce  3  qrs.  3  lb.  1  oz.  12f  dr.  to  the  fraction  of  a  cwt. 

Facit,  ^. 

65.  Reduce  1  oz.  4  dwts.  to  the  fraction  of  a  pound  troy. 

Facit,  |. 

66.  Reduce  2  qi-s,  3^  nails  to  the  fraction  of  an  English  ell. 

Facit,  f 

67.  Reduce  6  -fur.  16  poles  to  the  fraction  of  a  mile. 

Facit^.  1= 

68.  Reduce  2  roods  20  poles  to  the  fraction  of  an  acre. 

*  Facit,  f.' 

69^  Reduce  54  gallons  to  the  fraction  of  a  hogshead  of  wine. 

Facit,  f . 


It       112 


bubtbactionIof  vulgar  fractions. 


70.  Reduce  12  gallons  to  the  fraction  of  a  barrel  of  beer. 

Facit,  ^. 

71  Reduce  fifteen  bushels  to  the  fraction  of  a  chaldron  of  coals. 
^      *  #  Facit,  T*i. 

72.  Reduce  2  weeks,  2  days,  19  hours,  12  minut^,  to  the 
fraction  of  a  month.  ^^^^  «* 

ADDITION  OF  VULGAR  FRACTIONS. 

Rule.  Reduce  the  given  fractions  to  a  common  denominator, 
then  add  all  the  numerators  together,  under  which  place  the  com- 
mon denominator. 


EXAMPLES. 


Facit,  it +H=H=l7V 
Facit,  HH- 
Facit,  4^|.     c 
Facit,  8tV- 
Facit,  li.  . 


1.  Add  a  and  ^  together. 

2.  Add  I,  if  and  |  together. 

3.  Add  1,  4^  and  f  together. 

4.  Add  7|  and  |  together. 

5.  Add  ^  and  |  of  f  together. 

6.  Add  6i  6^  and  4i  together^,  Facit.  17^>^. 

2.   When  the  fractions  are  offeeveral  denominations,  reduce 
them  to  their  proper  quantity,  and  add  as  before. 

7.  Add  I  of  a  pound  to  I  of  a  shilling.  Facit,  ISs.  lOd. 

8.  Add  i  of  a  penny  to  |  of  a  pound.  Facit,  13s.  ^a. 

9.  Add  i  of  a  pound  troy  to  ^  of  an  ounce. 

Facit  9  oz.  3  dwts.  8  grs. 

10.  Add  I  of  a  ton  to  I  of  a  lb. 

Facit,  16  cwt.  0  qrs.  0  lb.  13  oz.  5  J  dr. 

11.  Add  I  of  a  chaldron  to  f  of  a  bushel. 

Facit,  24  bushels  3  pecks. 

12.  Add  i  of  a  yard  to  |  of  an  indi.         .    ^  „  ^ 

°  Facit,  C  inch.  2  bar.  corns. 

SUBTRACTION  OF  VULGAR  FRACTIONS. 

Rule.  Reduce  the  given  fraction  to  a  common  deuomiuator, 
then  subtract  the  less  numerator  from  the  greater,  a%d  place  the 
remainder  over  the  common  denominator. 


MULTIPLICATION.  1*13 

2.  When  the  lower  fraction  is  greater  than  the  upper,  sub- 
tract the  numerator  of  the  lower  fraction  from  the  denominator, 
and  to  that  ^fFerence  add  the  upper  numerator,  carrying  one  to 
the  unit's  place  of  the  lowei-  whole  number. 

EXAMPLES. 

1.  Fromftakef     3XV  =  21.    5X4=20.    21— 20=1  num. 

4X7  =  28  den.  Facit  J- 

2.  From  f  take  f  of  f .  Facitj  11 

3.  From  5^  take  -j?^.  Pacit,  4|5. 

4.  From  II  take  f  Facit,  ^<V 

5.  From  ^£  take  |  of  f .  Facit,  III. 

6.  From  64^  take  f  of  i  Faxjit,  elf. 

3.   When  the  fractions  are  of  several  denominations,  reduce 
them  to  their  proper  quantities,  and  subtract  as  before. 

7.  From  |  of  a  pound  take  ^  of  a  shilling.       Facit,  14s.  3d. 

8.  From  f  of  a  shilling  take  i  of  a  penny.  Facit,  T^d^ 

9.  From  |  of  a  lb.  troy  take  }  of  an  ounce.  ' 

^    ^  Facit,  8  oz.  16  dwte.  16  grs. 

10.  From  f  of  a  ton  take  |  of  a  lb. 

Facit,  15  cwt.  3  qrs.  2Y  lb.  2  oz.  lOf  drs. 

11.  From  f  of  a  chaldron,  take  |  of  a  bushel. 

,„   ^  ■  Facit,  23  bushels,  1  peck. 

12.  From^  of  a  yard,  take  |  of  an  inch. 

Facit,  6  in.  1  b.  com. 
MULTIPLICATION  OF  VULGAR  FRACTIONS. 

Rule.  Prepare  the  given  numbers  (if  they  require  it)  by  the 
rules  of  Reduction ;  then  multiply  all  the  numerators  together  for 
a  new  numerator,  and  all  the  denominators  for  a  new  denomin- 
ator. 


1. 


EXAMPLES. 
Multiply  I  by  f . 

Facit,  3X3=9  num. 
2.  Multiply  i  by  #. 
Multiply  48f  by  13f . 
430A 


Multiply 


by  18f 


6.  Multiply  if  by  i  of  f  of  | 
6.  Multiply  yL  by  f  of  f  of  f 


k3 


4X5=20  den.— JV. 

- "5    2  7' 

Facit,  672^^. 
Facit,  V935f f. 

Facit,  ■iji\=H' 
Facit,  f . 


/. 


114 


smOLE   SUUS    OF   THREE   DIBECT 


7.  Multiply  I  of  1  by  t  of  f 

8.  Multiply  i  of  §  by  4. 

9.  Multiply  54  by  I . 

10.  Multiply  24  by  f . 

11.  Multiply  i  of  9by  1. 

12.  Multiply  9i  by  f . 


Facit,  ^. 

Facit,  ^. 

^Facit,  m. 

Facit,  16. 

Facit,  5|f . 

Facit,  3j. 


DIVISION  OF  VULGAR  FRACTIONS. 

Rule.  Prepare  the  given  numbers  (if  they  require  it)  by  the 
rules  of  Reduction,  and  invert  the  divisor,  then  proceed  as  in 
Multiplication. 


EXAMPLES. 


;fc 


1.  Divide  ^y  by  f 

.     Facit,  6  X  9=45  num.  3  X  20= 

2.  Divide  II  by  f. 

3.  Divide  672^^  by  13f . 

4.  Divide  7935^1  by  18f 

5.  Divide  t  by  I  of  ^  of  f 

6.  Divide  |  of  16  by  4  of  i 
•  1.  Divide  i  of  |  by  f  of  i 

8.  Divide  9^^  by  i  of  1. 

9.  Divide  ^^  by  4^ 

10.  Divide  16  by  24. 

11.  Divide  5205^0  by  f  of  91. 

12.  Divide  d}  by  9^. 


:60  den.— H=|. 
Facit,  J. 
Facit,  48f 
Facit,  430f . 
Facit,  ^fiff. 
Faeis,  19  i\. 
Facit,  a|=|. 
Faqit,  2^^. 
Facit,  |. 
Facit,  f . 
Facit,  Ylf 
Facit,  ^. 


THE  SINGLE  RULE  OF  THREE  DIRECT,  IN  VULGAR 

FRACTIONS. 


Rule.  Reduce  the  numbers  as  befpfe  directe 
State  the  question  as  in  the  Rule  of  Three  m  whole  numbers  and 
invert  the  first  term  in  the  proportion,  then  multiply  the  three 
terms  continually  together,  and  the  product  will  be  the  answer. 


st^ohii  nvLiE  OP 'three  inverse. 


115 


■h 


EXAMPLES. 

1.  If  I  of  a  yard  cost  f  of  £1,  what  will  V>y  of  a  yard  come  to 
at  that  rate?  ^^^^  la^ig^, 

yd.    £     yd.       £ 
Asf  :  |::^y  :  |i  =  l5s. 

for  4X  5X9  =  180  num.        .      „       .      ,x      ,      „ 
and  3  X  8  X  10  =  240  den.  ^'*  ^X  A=U  fHf  (M^- 

2.  If  f  of  a  yard  cost  f  of  £l,  vfha,t  will  ji  of  a  yard  cost? 

Ans.  148.  8d. 

3.  If  I  of  a  yard  of  lawn  cost  Ts.  3d.,  what  will  10^  yards 
cost?  Ans.  £4  :  19  :  10||. 

4.  If  ^  lb.  cost  |s.  how  many  pounds  will  |  of  Is.  buy  ? 

Ans.  1  lb.^f^=^\. 

6.  If  I  ell  of  Holland  cost  J  of  £1,  what  will  12^  ells  cost  at 
the  same  rate  ?  Ans.  £7:0:8^  U. 

6.  If  12^  yards  of  cloth  cost  15s.  9d.,  what  will  48^  cost  at  the 
same  rate  ?  Ans.  £3  :  0  :  9^  j\\. 

I.  If  ^^  of  a  cwt.  cost  2848.  what  will  7^  cwt.  cost  at  the  same 

^^^  ^W5.  £118  :  6  :  8. 

8.  If  3  yards  of  broad  cloth  cost  £2 A,  what  will  10ft  yards 
cost?  Ans.  £9  :  12. 

9.  If  i  of  a  yard  cost  §  of  £l,  what  will  f  of  an  ell  English 
come  to  at  the  same  rate  ?  Ans.  £2. 

10.  If  1  lb.  of  cochineal  cost  £l  :  5,  what  will  S6j\  lb.  come 
^?  Jws.  £45  :  17  ;  6. 

II.  If  1  yard  of  broad  cloth  cost  l5fs.,  what  will  4  pieces  cost, 
each  containing  27f  yards?  Ans.  £85  :  14  :  3^  |f  or  4. 

12.  Bought  3^  pieces  of  silk,  each  containing  24f  ells,  at  6s. 
9|d.  per  ell.     I  desire  to  know  what  the  whole  quantity  cost  ? 

Ans.  £25  :  17  :  2^  ||. 

THE  SINGLE  RULE  OF  THREE  INVERSE,  IN 
VULGAR  FRACTIONS. 

EXAMPLES. 

1.  If  48  men  can  build  a  wall  in  24i  days,  how  many  men 
can  do  the  sAme  in  192  days ?  'Ans.  6-^^  men. 

2.  If  25if8.  will  pay  for  the  carriage  f^^  1  cwt.  146i  miles,  how 
for  may  ^^  cwt.  be  carried  for  the  same 


-s>ney 


Ans.  22^  miles. 


116 


THB  DOUBLE  RULE  OF  THRBB. 


3.  If  3\  yards  of  cloth,  that  is  1}  yard  wide,  be  sufficient  to 
make  a  cloak,  how  much  must  I  have  of  that  sort  which  is  f  yard 
Avide,  to  make  another  of  the  same  bigness ! 

Ans.  4 1  yards. 

4.  If  three  men  can  do  a  piece  of  work  in  4^  hours,  in  how 
many  hours  will  ten  men  do  the  same  work  ? 

Ans.  ly\  hour. 

5.  If  a  penny  white  loaf  weighs  1  oz.  when  a  bushel  of  wheat 
cost  5s.  6d.,  what  is  a  bushel  worth  when  a  penny  white  loaf 
weighs  but  2^  ozJ  •  ^ws.  16s.  4|d. 

6.  Whaf.  quantity  of  shalloon,  that  is  f  yard  wide,  will  line  H 
yards  of  cloth,  that  is  1^  yard  wide  ?  Ans.  15  yards. 

THE  DOUBLE  RULE  OF  THREE,  IN  VULGAR 

FRACTIONS. 

*  EXAMPLES. 

1.  If  a  carrier  receives  £2^^  for  the  carriage  of  3  cwt.  150 
miles,  how  much  ought  he  to  receive  for  the  carriage  of  1  cwt 
3^  qrs.  60  miles?  -^wa-  :6l  :  16  :  9. 

2.  If  £100  in  12  months  gain  £6  interest,  what  principal  will 
gain  £3f  in  9  months  ?  -^w*.  £76. 

3.  If  9  students  spend  £10|  in  18  days,  how  much  will  20 
students  spend  in  30  days  ?  Ans.  £39  :  18  :  4t\%\. 

4.  A  man  and  Lis  wife  having  laboured  one  day,  earned  4f  s. 
how  much  must  they  have  for  lOi  days,  when  their  two  sons 
helped  them?  Ans.  4  :  11  :  l^. 

5.  If  £50,  in  6  months,  gain  £2yV4.  "^^^^  ^^^  ^^^^  ^^^^  '^^ 
quire  to  gain  £1tV?  ^m.  9  months, 

C.  If  the  carriage  of  60  cwt.  20  miles  cost  £14^,  what  weight 
can  I  have  carried  30  miles  for  £5t\  ?  Ans.  15  cwt. 


117 


THE 


TUTOR'S    ASSISTANT. 


PART  III. 


DECIMAL  FRACTIONS.  • 

tn  Dedmal  Fractions  the  inteo'er  or  wIioIa  fJ.in„  ,.  '     , 

one  yard,  one  gallon,  &6.  fa  ,„^led  it  dWdfdlnr.rT""'^; 

Whole  numbers.     Decimal  parts. 


1  6 


o 

s 

CO 


S-g- 


t3^  CO 

CO    Orf 

!»    on 
B    " 


4321    ,2  34667 

g-  sr  g- s- ST  S- i- 

2>  2.  S  o  o  o 

e   S3  o     _  .  ,  Cii 


e- 


g 


a  2 

tr'  CO 

CO 


B 

CO 


g  § " 

i| 


sSiif^^j^iHrss 


tjg  ADDITION   OP   DECIMALS. 

before  decimri  parts  decrease  their  value  by  removing  them  far- 
S  from  the  comma,  or  unit's  place ;  thus,  ,5  is  6  parte  of  10,  or 
X  06  is  6  Paftsof  100.  "'  tJi!  .005  is  6  par  8  of  1000,  or 
„!;•  ,0005  is  6  parte  of  10000,  or  „H?-  »"Vn'".To  tc 
didmal  parts  do  not  alter  their  value.     For  ,6,  ,60,  ,500,  &c. 

"  a1'«  DlcfMl^i""t  which  ends  at  a  certain  number  of 

nlaces  but  an  infinite  is  that  which  no  where  ends. 

^  A  kECunaiNO  bkcimal  is  that  wherein  one  or  more  figures 

'^A:d'Si'527^2?6''is".SwT-ooMPOUNi>  KBCuaaiNa  .koi- 

MAL. 

Note.   A  finite  deciraal  may  be  considered  as  ;nfi"^tej)y  ma- 
king ciphers  to  recur;  for  they  do  not  alter  the  value  of  the  deci- 

""In  all  operations,  if  the  result  consiste  of  several  nines    reject 
them,  and  make  the  next  superior  place  an  umt  more;  thus,  tor 

26,25999,  write  26,  26.  ,    ,    ,     ,    ^  ^ 

In  all  circulating  numbers,  dash  the  last  tigure. 


ADDITION  OF  DECIMALS. 

Rni.B  In  settin"  down  the  proposed  numbers  to  be  added, 
„^r^re  muTbe"  taken  in  plilcin^g  every  figure  directly  under- 
ShXw  the  same  value,  whether  they  be  mixed  numbe.^, 
rSre  decimal  parte;  and  to  perform  which  there  in-t  be  a  due 
ZLi  had  to  the  ««mas,  or  separating  pomts,  which  ought 
Sp  tostand  injilrect  line,  one  under  another,  and  t/^  4e 


le  G^i 
iii^^Tii 
emcare 


SThandTth  r^^rSyliaee  the  decimal  parte  acco..,ng 
KeS  respective  values;  then  add  them  as  m  whole  numb  .:. 

EXAMPLES. 

1.  AddV||fr3.^Zi.+2,15U+8t.   '+2.V|^.^_  ,3o_3,3,. 

2,  Add  30,0'?4  '-',0O7H-59,432+7,l.    _ 
8.  Add  3,6+i7,25+9'27,Ol+2,0073-hi,&. 
4    Add  62,76+47,21  +  724  +  31,452+8075. 
6.  Add  3275+27,514+1,005+725+7  32. 
6.  Add27,5+52+3,2676+,5741+2720. 


MULTIPLIOATIOIf   OF    DECIMALS. 


M 


SUBTRACTION  OF  DECIMALS. 

RuLK.  Subtraction  of  decimlfs  diflfers  but  littlo  from  whole 
numbers,  only  in  placing  the  numbers,  which  must  be  carefully 
observed,  as  in  addition. 


EXAMPLES. 


1.  From  ,2764  take      ,2371. 

2.  Froiii  2,37  take  1,76. 
?.  From  271  take  215,7. 
4.  From  270,2  take  75,4075. 


6.  From       671  take  64,72. 

6.  From       625  take  76,91. 

7.  From  23.415  take  ,3742. 

8.  From      ,107  take  ,0007 


MULTIPLICATION  OF  DECIMALS. 


.)•>: 


Rule.  Place  the  factors,  and  multiply  them,  as  in  whole  num- 
bers, and  from  the  product  towards  the  right  hand,  cut  off  as 
many  places  for  decimals  as  there  are  in  both  factors  together; 
but  if  there  should  not  be  so  many  places  in  the  product,  sup- 
ply th«  defect  with  ciphers  to  the  left  hand. 


EXAMPLES 


1.  Multiply 

2.  Multiply 

3.  Multiply 

4.  Multiply 

5.  Multiply 

6.  Multiply 


,2365  by  ,2435.  Facit,  ,05758775. 


2071  by  2,27. 

27,15  by  25,3. 
72347  by  23,15. 
17105  by  ,3257. 
17105  by  ,0237. 


7.  Multiply  27,35  by  7,70071.- 

8.  Multiply  67,21  by  ,0075. 

9.  Multiply    ,007  by  ,007. 

10.  Multiply  20,15  by  ,2705. 

11.  Multiply    ,907  by  ,0025. 


When  any  nui^er  of  decimals  is  to  be  multiplied  by  10,  100, 
1000,  (fee,  it  is  01%  remo\dng  the  separating  point  in  the  raulti- 
pUcand  so  many  places  towards  the  right  hand  as  there  are  ciphers 
in  the  multiplier:  thus,  ,578X10—5,78.  ,578X100=5,78 ;,  578 
X  1000=578;  and  ,578X10000=5780. 

CONTRACTED  MULTIPLICATION  OF  DECIMALS. 

Rule.  Put  the  unit's  place  of  the  multiplier  under  that  place 
of  the  multiplicand  that  is  intended  to  be  kept  in  the  product,  then 
invert  the  order  of  all  the  other  figures,  i.  e.  write  them  all  the 


120 


CONTRACTED    MULTIPLICATION. 


contrary  way ;  and  in  multiplying,  begin  at  tlie  figure  m  the  mul- 
tiplicand, which  stands  over  the  figure  you  are  then  multiplying 
with,  and  set  down  the  first  figure  of  each  particular  product  di- 
rectly one  under  the  other,  and  ^ve^  due  regard  to  the  increase 
arising  from  the  figures  on  the  right  hand  of  that  figure  you  begin 
to  multiply  at  in  the  multiplicand. 

Note.  That  in  multiplying  the  figure  left  out  every  time  next 
the  right  hand  in  the  multiplicand,  and  if  the  product  be  6,  or 
upwards,  to  15,  carry  1 ;  if  15,  or  upwards,  to  25,  carry  2;  and 
if  25,  or  upwards,  to  35,  carry  3,  «fcc. 


0 


EXAMPLES. 


12.  Multiply  384,672158  by  36,8346,  and  \ei  there  be  only 
four  places  of  decimals  in  the  product. 


Contracted  way. 
384,672158 
5438.63 

115401647 

23080330 

307737t 

115402 

15387 

1923 

14169,2065 


Common  way. 
384,672158 
36,8345 


1923 

15386 

115401 

3077377 

23080329 

115401647 


360790 

88632 

6474 

264 

48 

4 


14169,2066 


038510 


Facit,  14169,2066. 


13.  Multiply  3,141592  by  52,7438,  and  leave  only  four  places 
of  decimals.  f^^^^^^  165,6994. 

.     14.  Multiply  2,38645  by  8,2175,  and  leave  only  four  places 
of  decimals.  F^^^*'  l^'^^^^' 

15.  Multiply  375,13758  by  167324,  and  let  there  be  only  one 
Place  of  decimals.  Facit,  6276,9. 

16.  Multiply  375,13758  by  16,7324,  and  H*^«.<^"]y  Jf^^  P^^^ 
of  decimals.  Facit,  6276,9520. 

17.  Multiply  395,3756  by  ,76642,  and  let  there  ^^  o£y^*<>^'f 
places  of  decimals.  Facit,  299,0699. 


le  mul- 
:iplying 
luct  di- 
mcrease 
u  begin 


ne  next 
>e  6,  or 
2;  and 


be  only 


DIVISION   OP   DECIMALS.  121 


DIVISION  OF  DECIMALS. 

finJf'^-  ^""^^  J8. also  worked  as  in  whole  numbers;  the  only  dif- 
lowinyrX  :   "'"^        '^'''^^'''''  ""^^^  ''  ^"°"  ^^  ^"^  ^^  *^^  ^'^l- 

RuLE  1.    The  first  figure  in  the  quotient  is  always  of  the  same 

ot'thTi^'f'n"•'^^/^^^^^^^  ^^^^^  ---  -'^^ 

over  the  place  of  units  m  the  divisor. 

a.  ?^  The  quotient  must  always  have  so  many  decimal  places 
as  the  dividend  has  more  than  the  divisor.  ^        * 

hJ^^A  ^'    Y  *^!  ^'r^*'  ^"'^  ^^^^^°^  ^^^«  lt>«tl^  the  same  num- 
ber  of  decimal  parts,  the  quotient  will  be  a  whole  number. 

3.  But  if,  when  the  division  is  done,  the  quotient  has  not  so 

ZhlJ^Zt:^  ''  f'f^  ^r  P^«^^^  ^f  ^''^^^  then  so  man; 
-^iphers  must  be  prefixed  as  there  are  places  wanting.  ^, 


EXAMPLES. 


) 
,2065. 

ir  places 
,6994. 

ir  places 
,6107. 

only  one 
276,9. 

ur  places 
,9520. 

)nly  four 
,0699.  \r 


1.  Divide  85643,825  by  6,321. 


2.  Divide  48  by  144 

3.  ^Divide  217,75  by  65. 

4.  Divide  125  by  ,1045. 

5.  Divide  709  by  2,574. 

6.  Divide  5,714  by  8275. 


I, 


m 


r.  Divide  7382,54  by  6,4252. 

8.  Divide  ,0851648  by  423. 

9.  Divide  267,15975  by  13,25. 

10.  Divide  72,1564  by  ,1347. 

11.  Divide  715  by  ,3076. 


Vyiien  numbers  are  to  be  divided  by  10,  100,  1000    10000 

so  many  places  towards  tliA  l^ft  har,A    o«  *u^t --.i        .    ., 

divisor."  "  '"^'*  '*°  """""^  "*"  wpiiers  m  tne 


Thus,  5784-^  10=578,4. 
5784-M00=57,84. 


5784~-    1000=5,784. 
6784-M0,000=,5784. 


3«3 


CONTRACTED    DIYISIOW. 


CONTRACTED  DIVISION  OF  DECIMALS. 

Rule.  By  the  first  rule  find  what  is  'the  value  of  the  first  figure 
in  the  quotient:  then  by  knowing  the  first  figure's  denomination, 
the  decimal  places  may  be  reduced  to  any  number,  by  taking  as 
many  of  the  left  hand  figures  of  the  dividend  as  will  answer  them ; 
and  in  dividing,  omit  one  figure  of  the  divisor  at  each  following 
operation. 

Note.  That  in  multiplying  every  figure  left  out  in  the  divisor, 
you  must  carry  1,  if  it  be  5  or  upwards,  to  15  ;  if  15,  or  upwards, 
to  25,  carry  2  ;  if  25,  or  upwards,  to  35,  carry  3,  &c. 

EXAMPLES. 
12.  Divide  '721,1'7562  by  2,257432,  and  let  there  be  only  three 
places  of  decimals  in  the  quotient.    ! 

Contracted.  Common  way. 

2,257432)721,17562(319,467  2,257432)721,17562(319,467 

6772296  6772296 


439460 
225743 

213717.. 
203169.. 

10548... 
9030... 


1518.... 
1354. ... 


164 
168 


6 


■  t  Hi  H  rTit 
Oli  i.  iOVL 


13.  Divide  8,758615  by  5,2714167. 

14.  Divide 

15.  Divide 

16.  Divide 

17.  Divide 

18.  Divide 


439460 

2 

225743 

2 

213717 

00 

203168 

88 

10548 

120 

9029 

728 

1518 

3920 

1354 

4592 

163 

93280 

158 

02024 

•       5 

91256 

25,1367  by  217,35. 
51,47542  by  ,123415. 
70,23  by  7,9863. 
27,104  by  3,712. 


UEDUCflON    OP   DECIMALS. 


128 


5t  figure 
lination, 
iking  as 
r  them ; 
allowing 

)  divisor, 
ipwards, 


aly  three 


[319,467 


2 
2 

00 

88 

120 

728 

3920 
4592 

93280 
02024 

91256 


REDUCTION  OF  DECIMALS. 

To  reduce  a   Vulgar  Fraction  to  a  Decimal. 


% 


Rule.   Add  ciphers  to  the  numerator,  and  divide  by  the  de- 
nominator, the  quotient  is  the  decimal  fraction  required. 

EXAMPLES 

1.  Reduce  ^ to  a  decimal.  4)1,00(25  Facit. 

2.  Reduce  ^ to  a  decimal.  Facit    5 

3.  Reduce  f to  a  decimal.  Facit  '75* 

4.  Reduce  f to  a  decimal.  Facit,  ',375.' 

5.  Keduce  ^\ to  a  decimal.  Facit,  ,1923076+. 

6.  Reduce  J-i  of  |f  .  to  a  decimal.  Facit,  ,6043956+. 

Note.  If  the  given  parts  are  of  several  denominations,  they 
may  be  reduced  either  by  so  many  distinct  operations  as  there 
are  different  parts,  or  by  first  reducing  them  into  their  lowest 
denomination,  and  then  divide  as  before ;  or, 

2ndly.  Bring  the  lowest  into  decimals  of  the  next  superior  de- 
nomination, and  on  the  right  hand  of  the  decimal  found,  place  the 
parts  given  of  the  next  superior  denomination ;  so  proceedino-  till 
you  bring  out  the  decimal  parts  of  the  highest  integer  required,  by 
still  dividing  the  product  by  the  next  superior  denominator ;  or, 

3dly.  To  reduce  shillings,  pence,  and  farthings.  If  the  num. 
ber  of  shillings  be  even,  take  half  for  the  first  place  of  decimals, 
and  let  the  second  and  third  places  be  filled  with  the  ferthirif^s 
contained  in  the  remaining  pence  and  farthings,  always  remem- 
bering to  add  1,  when  the  number  is,  or  exceeds  25.  But  if  the 
number  of  shillings  be  odd,  the  second  place  of  decimals  must 
be  increased  by  5. 

'7.  Reduce  5s.  to  the  decimal  of  a  £.  Facit,  ,26. 

8.  Reduce  9s.  to  the  decimal  of  a  £.  Facit',  [45! 

9.  Reduce  16s.  to  the  decimal  of  a  £.  Facit!  ,8! 

l3 


124  SEDUCTION   OF   DECIMALS. 

10.  Reduce  8s.  4cl.  to  the  decimal  of  a  £. 
11  ^Reduce  168.  Tfd.  to  the  decimal  of  a  £. 


first. 
168.  I^d. 
12 

,    199 
4 

960)799(8322916 


second. 
4)3,00 

12)7,76 


third. 
2)16 

,832 


Facit,  ,4166. 

Facit,  ,8322916. 

7|d. 
4 


2iO)16,64583 
,8322916 


31 


r 


l 


12.  Reduce  19s.  S^d.  to  the  decimal  of  a  £. 

Facit,  972916. 

13.  Reduce  12  grains  to  the  decimal  of  a  lb.  troy. 

Facit,  ,002083. 

14.  Reduce  12  drams  to  the  decimal  of  a  lb.  avoirdupois. 

Facit,  ,046875. 

16.  Reduce  2  qrs.  14  lb.  to  the  decimal  of  a  cwt. 

Facit,  ,625. 

16.  Reduce  two  furlongs  to  the  decimal  of  a  league. 

Facit,  ,0833. 

17.  Reduce  2  quarts,  1  pint,  to  the  decimal  of  a  gallon. 

Facit,  ,626. 

18.  Reduce  4  gallons,  2  quarts  of  wine,  to  the  decimal  of  a 
hogshead.  Facit,  ,071428+. 

19.  Reduce  2  gallons,  1  quart  of  beer,  to  the  decimal  of  a  bar- 
rel. Facit,  ,0625. 

20.  Reduce  62  days  to  the  decimal  of  a  year. 

Facit,  ,142465+. 

To  find  the  valite  of  any  Decimal  Fraction  in  the  known  parts 

of  an  Integer. 

Rule.  Multiply  the  decimal  given,  by  the  number  of  parts  of 
the  next  interior  denomination,  cutting  off  the  decimals  from  the 
product ;  then  multiply  the  remainder  by  the  next  inferior  deno- 
mination; thus  pioceeding  till  you  have  brought  in  the  least 
known  parts  of  an  integer. 


■'>«iiiffiftBir.ii'aifri-tii,ii 


II  ll«.lwil.ll  I  ■^^' 


BEDUCTION   OP   DECIMALS. 


125 


EXAMPLES. 

21.  What  is  the  vahie  of  ,8322910  of  a  lb.  ? 

Ans.  16s.  7id.-f . 


20 


16,6458320 
12 

7,7499840 
4 

2,9999360 


22.  What  is  the  value  of  ,002084  of  a  lb.  troy  ? 

Ans.  12,00384  gr. 

23.  What  is  the  value  of  ,046875  of  a  lb.  avoirdupois  ? 

Ans.  12  dr. 

24.  What  is  the  value  of  ,625  of  a  cwt.  ? 

Ans.  2  qrs.  14  lb. 

25.  What  is  the  value  of  ,625  of  a  gallon  ? 

Ans.  2  qrs.  1  pint 

26.  What  is  the  value  of  ,071428  of  a  hogshead  of  wine  ? 

Ans.  4  gallons  1  quart,  ,999856. 

27.  What  is  the  value  of  ,0625  of  a  barrel  of  beer  ? 

Ans.  2  gallons  1  quart 

28.  What  is  the  value  of  ,142465  of  a  year  ? 

Ans.  51,999725  day^. 


126 


il 


h: 


¥1 
m 


DECIMAL    TABLES    OP    COIN,    WEIGHT,    AND    MEASURE. 


TABLE  I. 
English  Coijv. 


£  1  the  Integer. 


Sh. 

19 

18 

17 

16 

15 

14 

13 

12 

11 

10 


Dec. 
,93 
,9 
,S3 
,8 
,73 
,7 
,63 
,6 
,53 
,5 


Sh. 
9 
8 
7 
6 
5 
4 
3 
2 
1 


Dec. 
,45 
,4 
,35 
,3 
,25 
,2- 
,15 
.1 
,05 


Pence. 
6 
5 

-■'  4 
3 
2 
1 


Decimals. 
,025 
,020833 
,016666 
,0125 
,008333 
,004166 


Farth. 
3 
2 
1 


Decimals. 
,003125 
,0020833 
,0010416 


TABLE  n. 

English  Coin.    1  Sh. 

Long  Measure.  1  Foot, 
the  Integer. 


Pence  & 
Inches. 
6 

IS 

O 

4 
3 
2 
1 


Decimals. 
,5 

,333333 
,23 

,166666 
,083333 


Faith. 
3 
2 
1 


Decimals. 
,0625 
,041666 
,020833 


TABLE  III. 

Troy  Weight. 

1  lb.  the  Integer.. 

Ounces  the  same  as 
Pence  in  the  last 
Table. 


Dwts. 
10 
9 
8 
7 
6 
5 
4 
3 
2 
1 


Decimals. 
,041666 
,0375 
,033333 
,029166 
,023 
,020833 
,016666 
,01,25 
,008333 
,004166 


Grains. 
12 
11 
10 

9 

8 

7 

6 

5 

4 

3 

2 

1 


Decimals. 

,002083 
,001910 
,001736 
,001562 
,001389 
,001215 
,001042 
,000868 
,000694 
,000521 
,000347 
,000173 


1  oz.  the  Integer. 


Pennyweights  the  same 

as  Shillings  in  the  first 
Table. 


Grains. 
12 
11 
10 

9 

8 

7 

6 

5 

4 

3 

2 

1 


Decimals. 
,052 
,022916 
,020833 
,01875 
,016666 
,014583 

',0125 
,010416 
,008333 
,00625 
,004166 
,002083 


TABLE  IV. 
Avoir.  Weight. 

112  lbs.  the  Integer. 


Qrs. 

Decimals. 

3 

,75 

2 

,5 

1 

,25 

Pounds. 
14 
13 
12 
11 
10 

9 

8 

7 

6 

5 

4 

3 

o 

a 

1 


Decimals. 
,125 
,116071 
,107143 

,098214 

,089286 

,080357 

,071428 

,0625 

,053571 

,044643 

,035714 

,026786 

,008928 


Ounces. 

•  8 
7 


Decimals. 

,004464 
,003906 


127 


3ASURE. 


Decimals. 
,052 
,022916 
,020833 
,01S75 
,016066 
,014583 

',0125 
,010416 
,008333 
,00625 
'  ,004166 
,002083 


BLE  IV. 
.  Weight. 
the  Integer. 


Decimals. 
,75 
,5 
,25 

Decimals. 
,125 
,116071 
,107143 

,098214 

,089286 

,080357 

,071428 

,0625 

,053571 

,044643 

,035714 

,026786 

,ui  ioo s 

,008928 


Decimals. 

,004464 
,003906 


DECIMAL    TABLES    OF    COIN,    WEIGHT,    AND    MEASURE. 


4 

3 

o 

1 


,003348 
,002790 
,002232 
,001674 
,001116 
,000558 


k  Oz. 
3 
2 
1 


Decimals. 
,000418 
,000279 
,000139 


TABLE  V. 

AvOIRDli^'OIS  WEIGHT. 

1  lb.  the  Integer. 


Ounces. 
8 
7 
H 
5 
4 
3 
2 
1 


Decimals. 
,5 

,4375 
,375 
,3125 
,25 
,1875 
,125 
,0025 


Drams. 
8 
7 
6 
5 
4 
3 
2 
1 


Decimals. 
,03125 
,027343 
,023437 
,019531 
,015625 
,011718 
,007812 
,003906 


TABLE  VL 


lilQiriD   MEASURE 


1  tun  the  Integer. 


Gallons. 
100 
90 


Decimals. 
,390825 
,357142 


80 

70 

00 

50 

40 

30 

20 

10 

9 

8 

7 

6 

5 

4 

3 

2 

1 


,317400 

,27 

,238095 

,198412 

,158730 

,119047 

,079365 

,039082 

,035714 

,031740 

,027 

,023809 

,019841 

,015873 

,011904 

,007930 

,00396s 


Pints. 
4 
3 
2 
1 


A 

Hogshead  the 
Integer. 


Gallons. 
30 
20 
10 

9 

8 

7 

6 

5 

4 

3 

2 

1 


Tints. 
3 
2 
1 


Decimals. 
,005952 
,003968 
,001984 


Decimals. 

,001984 
,001483 
,000992 
,009496 


TABLE  yil. 

Measures. 

Liquid.  Dry. 

1  Gal.  1  Qr. 

Integer. 


Pts. 
4 
3 
2 
1 


Decimals. 
,5 

,375 
,25 
,125 


Decimals. 

,476190 
,317460 
,158730 
,142857 
,126984 
,111111 
.095238 
,079365 
,063492 
,047619 
,031746 
,015873 


Q.pt. 
3 
2 
1 


Decimals. 
,09375 
,0625 
,03125 


Decimals. 
,0234375 
,015625 
,0078125 


Decimals. 
,005859 
,003906 
,001953 


TABLE  VIL. 


Long  Measure. 


1  Mile  the  Integer. 


Yards. 
1000 
900 
800 
700 
600 


Decimals. 
,^568 182* 
,511364 
,454545 
,397727 
,340909 


128 


DECIMAL  TABLES  OF  COIN,  WEIGHT,  AND  MEASURE. 


5UU 

400 

300 

200 

100 

90 

80 

70 

CO 

50 

40 

30 

20 

10 

9 

8 

7 

0 

5 

4 

3 

2 

1 


,284091 
,227272 
,170454 
,113630 
,056818 
,051136 
,015451 
,039773 
,034091 
,028409 
,022727 
,017045 
,011364 
,005682 
,005114 
,004545 
,003977 
,003409 
,002841 
,002273 
,001704 
,001138 
,000568 


Feet. 
2 
1 


Decimals. 

,0003787 
,0001894 


Inches. 
6 
3 
1 


Decimals. 

,0000947 
,0000474 
,0000158 


TABLE  IX. 

Time. 

1  year  the  Integer. 

Months  the  same  as 
Pence  in  the  second 
Table. 


Davs 
365 
300 
200 
100 
90 


Decimals. 

i,6bo6oo 

,821918 
,547945 
,273973 
,246575 


80 

70 

60 

50 

40 

30 

20 

10 

9 

8 

7 

6 

5 

4 

3 

2 

1 


,219178 
,191781 
,164383 
,136986 
,109559 
,082192 
,054794 
,027397 
,024657 
,021918 
,019178 
,016438 
,013698 
,010959 
,008219 
,005479 
,002739 


1  day  the  Integer. 


Hours. 
12 
11 
10 

9 

8 

7 

6 

5 

4 

3 

2 

1 


Decimals. 


.5 


,458333 

,416666 

,375 

,333333 

,291666 

,25 

,208333 

,166666 

,125 

,083333 

,041666 


Minutes. 
30 
20 
10 

9 

8 

7 

6 

5 
4 
3 
2 
1 


Decimals. 
,020833 
,013888 
,006944 
,00.625 
,005555 
,004861 

^004166 
,003472 
,002777 
,002083 
,001389 
,000664 


TABLE  X. 

Cloth  measure. 

1  yard  the  Integer. 

Quarters  the  same  as 
Table  4. 


ails. 

Decimals 

2 

,125 

1 

,0025 

TABLE  XI. 

Lead  Weight. 

A  Foth.  the  Integer. 


Hund. 
10 
9 
d 
7 
6 
5 
4 
3 
2 
1 


Decimals. 
,512820 
,461538 
,410256 
,358974 
,307692 
,256410 
,205128 
,153846 
,102564 
,051282 


Qrs. 
2 
1 


Decimals. 

,025641 
,012820 


Pounds. 
14 
13 
12 
11 
10 

9 

8 


4 
3 

Q 


Decimals. 
,0064102 
,0059523 
,0054945 
,00503r>6 
,0045787 
,0041208 
,0036630 
,0032051 

r\r\nri  Ann 

16022898 
,0018315 
,00137^6 
,00091^7 
,0004578 


THE    RULE    OF   THBEE   IN   DECIMALS.  129 


■fjfj' 


THE  RULE  OF  THREE  IN  DECIMALS. 

EXAMPLES. 

If  26^  yards  cost  £3  :  16  :  3,  what  will  32^  yards  come  to? 

Ans.  £4  :  12  :  9i. 

yds.         £  yds. 

26,5  :  3,8125  :  :  32,25  : 
32,25 


26,5)122,953125(4,63974=£4  :  12  :  9^. 

2.  What  will  the  pay  of  540  men  come  to,  at  £l  :  5  :  6  per 
i"»n?  ^W5.  £688  :  10. 

3.  If  Vf  yards  of  cloth  cost  £2:12:9,  what  will  140|  yards 
of  the  same  cost  ?  ^W5.  £47  :  16  :  3  2,4  qrs. 

4.  If  a  chest  of  sugar,  weighing  1  cwt.  2  qrs.  14  lb.  cost  £36  : 
12  :  9,  what  will  2  cwt.  1  qr.  21  lb.  of  the  same  cost? 

Ans.  £11  :  14  :  2  3,5  qrs. 
6.  A  grocer  buys  24  ton  12  cwt.  2  qrs.  14  lb.  12  oz.  of  tobac- 
co for  £3678  :  6  :  4,  what  will  1  oz.  come  to?  Ans.  Id. 

6.  What  will  326^  lb.  of  tobacco  come  to,  when  1|  lb.  is  sold 
for  3s.  6d.  ?  Ans.  £38:1:  3. 

7.  What  is  the  worth  of  19  oz.  3  dwts.  5  grs.  of  gold,  at  £2  : 
19  per  oz.?  Ans.  £56  :  10  :  5  2,99  qrs. 

8.  What  is  the  worth  of  827f  yards  of  painting,  at  lO^d.  per 
yard?  ^W5.  £36  :  4  :  3  1,5  qrs. 

9.  If  I  lent  my  friend  £34  for  f  of  a  year,  how  much  ought  he 
to  lend  me  y\  of  a  year  to  requite  my  kindness  ?  Ans.  61. 

10.  If  f  of  a  yard  of  cloth,  that  is  2^  yards  broad,  make  a  gar- 
ment, how  much  that  is  |  of  a  yard  wide  will  make  the  same  ? 

Ans.  2,1 093 '75  yards. 

11.  If  1  ounce  of  silver  cost  5s.  6d.,  wkat  is  the  price  of  a  tan- 
kard that  weighs  1  lb.  10  oz.  10  dwts.  4  grs.  ? 

i'  Ans.  £6  :  3  :  9  2,2  qrs. 

12.  If  1  lb.  of  tobacco  cost  15d.  what  cost  3  hogsheads,  weigh- 
ing together  15  cwt.  1  qr.  19  lb.  ?  Ans.  £107  :  18  :  9. 

13.  if.  1  cwt.  of  currants  cost  £2:9:6,  what  will  45  cwt.  3 
qrs.  14  lb.  cost  at  the  same  rate?  Ans.  £113  :  10  :  9#. 

14.  Bouofht  6  chests 


cwt.,  what  do  they  come  to  ? 


sugar,  each  6  cwt.  3  qrs.  at  £2  :.16  per 


Ans,  £113  :  8. 


M\ 


1 1 

II 


il 


:{ sir 


130 


BXTBAGTION   OF   THB    SaVARB    I109T. 


15.  Bought  a  tankard  for  £10  :  12,  at  the  rate  of  68.  4d.  per 
ounce,  ^\  hat  was  the  weight  ? 

Jns.  39  oz.  15  dwts. 

16.  Gave  £187  :  3  :  3,  for  25  cwt.  3  qi-s.  14  lb.  of  tobacco, 
at  what  rate  did  I  buy  it  per  lb.  ? 

Ans.  Is.  3id. 

17.  Bouorht  29  lb.  4  oz.  of  coffee,  for  £10  :  11  :  3,  what  is  the 
value  of  3  lb.  ?  Ans.  £1:1:8. 

18.  If  I  give  Is.  Id.  for  3^  lb.  cheese,  what  will  be  the  value 
of  1  cwt.?  ^ws.  £1  :  14  :  8. 


EXTRACTION  OF  THE  SQUARE  ROOT. 

Extracting  the  Square  Root  is  to  find  out  such  a  number  as,  being 
multiplied  into  itself,  the  product  will  be  equal  to  the  given  num- 
ber. 

Rule.  First,  Point  the  given  number,  beginning  at  the  unit's 
place,  then  proceed  to  the  hundreds,  and  so  upon  every  second 
figure  throughout. 

Secondly.  Seek  the  greatest  square  number  in  the  first  point 
towards  the  left  hand,  placing  the  square  number  under  the  first 
point,  and  the  root  thereof  in  the  quotient;  subtract  the  square 
number  from  the  first  point,  and  to  the  remainder  bring  down 
the  next  point  and  call  that  the  resolvend. 

Thirdly.  Double  the  quotient,  and  place  it  for  a  divisor  on  the 
left  hand  of  the  resolvend ;  seek  how  often  the  divisor  is  contain- 
ed in  the  resolvend;  (preserving  always  the  unit's  place)  and  put 
the  answer  in  the  quotient,  and  also  on  the  right-hand  side  of  the 
divisor ;  then  multiply  by  thg  figure  last  put  in  the  quotient,  and 
subtract  the  product  from  the  resolvend;  bring  down  the  next 
point  to  the  remainder  if  there  be  any  more)  and  proceed  as  be- 
fore. * 


Roots. 


o,- 


^  ilTiS. 


1.  2.  3.     4.     5.     6.     7.     8      9. 

4.  0    "a.  25.  3fi.  ^%  6?     P-\. 


EXTSACTION  OF  THE  SaUARB  BOOT.  I        131 

Ans.  346. 


EXAMPLES. 
1.  What  is  the  square  root  of  119025  ? 


119025(345 


64)290 
256 

685)3425 
3425 


2.  What  is  the  square  root  of  106929  ?  Ans.  327+. 

3.  What  is  the  square  root  of  2268741  ?       Am.  1506,23 -f. 

4.  What  is  the  square  root  of  759679^  ?  \Ans.  2756,228+ 

5.  What  is  the  square  root  of  36372961  ?**»        Ans.  6031. 

6.  What  is  the  square  root  of  22071204  ?  Ans.  4698. 

When  the  given  number  consists  of  a  whole  number  and  deci- 
mals together,  make  the  number  of  decimals  even,  by  adding  ci- 
phers to  them ;  so  that  there  may  be  a  point  fall  on  the  unit's 
place  of  the  whole  number. 


.7.  What  is  the 

8.  What  is  the 

9.  What  is  the 

10.  What  is  the 

11.  What  is  the 

12.  What  is  the 


square 
square 
square 
square 
square 
square 


root  of 
root  of 
root  of 
root  of 
root  of 
root  of 


3271,4007? 

4795,25731? 

4,372594? 

2,2710957? 

,00032754? 

1,270059? 


Ans.  57,19+. 

^w*.  69,247+. 

Ans.  2,091 -f. 

Ans.  1,50101+. 

Ans., 01809 -i-^ 

Ans.  1,1269  + 


To  extract  the  Square  Moot  of  a  Vulgar  Fraction. 

Rule.  Reduce  the  fraction  to  its  lowest  terms,  then  extract 
the  square  root  of  the  numerator,  for  a  new  numerator,  and  the 
squiiai  root  of  the  denominator,  for  a  new  denominator. 

If  m^  fraction  be  a  surd  (i.  e)  a  number  where  a  root  can  ne- 
ver l^e  exactly  found,  reduce  it  to  a  decimal,  and  extract  the  root 
from  it. 


EXAMPLES. 


13.  What  is  the  square  root  of  f  f  |f  ? 

14.  What  is  the  square  root  of  f  f  f  a  ? 

15.  Wh.'it  is  the  square  root  of  tVt-'A? 


»  9  fi  ■»  4 


Ans.  f . 
Ans.  |. 
Ans.  4- 


at 

I 


ii 

;1 


liB 


•i' 


Ml 


EXTRACTION   OF   THS    SaUARB    ROOT. 


BURDB. 


16.  What  is  the  square  root  of  |ff  ? 

17.  What  is  the  square  root  of  |4^  ? 

18.  What  is  the  square  root  of  }Jf  ? 


Arts.  ,898024-. 
Ana.  ,86602+. 
Ans.  ,933094-. 


To  extract  the  Square  Root  of  a  mixed  number. 

Rule.  Reduce  the  fractional  part  of  a  mixed  nuraber  to  ita 
lowest  term,  and  then  the  mixed  number  to  an  improper  fraction. 

2.  Extract  the  root  of  the  numerator  and  denominator  for  a 
new  numerator  and  denominator.  • 

If  the  mixed  number  given  be  a  surd,  reduce  the  fractional 
part  to  a  decimal,  annex  it  to  the  whole  number,  and  extract  the 
square  root  therefrom. 

EXAMPLES. 


19.  What  is  the  square  root  of  5lf-}  ? 

20.  What  is  the  square  root  of  27/^  ? 

21.  What  is  the  square  root  of  9a| 


SURDS. 


22.  What  is  the  square  root  of  85|f  ? 

23.  What  is  the  square  root  of  8^  ? 

24.  What  is  the  square  root  of  6|  ? 


Ans.  7}. 
Ans.  b\. 
Ans.  Z\. 


Ans.  9,27-|-. 
Ans.  2,95194-. 
Ans.  2,6819  +  . 


To  find  a  mean  proportional  between  any  two  given  numbers. 

Rule.   The  square  root  of  the  product  of  the  given  number 
.  is  the  mean  proportional  sought. 

EXAMPLES. 

5.  What  is  the  mean  proportional  between  3  and  121 
Ans.  3  X  12  =  36,  then  fj  36  =  6  the  mean  proportional. 

6.  What  is  the  mean  proportional  between  4276  and  842  ? 

Ms.  1897,4  + 

To  find  the  side  of  a  square  equal  in  area  to  any  given 

superficies. 

Rule.   The  square  root  of  the  content  of  any  given  superficies 
is  the  side  of  the  square  equal  sought. 


inator  for  a 


■XTRAOTION  OP  THE  SQUABB  HOOT. 

EXAMPLES. 


133 


27.  If  the  content  of  a  given  circle  be  160,  what  is  the  side  of 
the  square  equal?  ^n^.  12,64911. 

eouaH  ^^  ^^^  ^'"^  ""^  *  ""'""^^  ^  ^^^'  ""^^^  ^  *^®  «*^«  «^  t^«  square 
^  ^w«.  27,38612. 

The  area  of  the  circle  given  to  find  the  Diameter, 
Rule.   As  355  :  452,  or,  as  1  :  1,273239  :  :  so  is  the  area  :  to 

Leabrri2l37^ntr''"'r';  "s^^a^^^  «^"^-  ^^^'-^'^^ 

area  Dy  1,12837,  ana  the  product  will  be  the  diameter 

vV 

EXAMPLES.  . 

oth!r"»nT/'  ^r^Y  ""^  T"  ^  "'  to  tie  to  a  cow's  tail,  the 
an  ITS"*  '"  '^  ^™""'^'  '^  '^'  ■>«'  have  liberty  of  e;tinK 

t/j  jeuus »  ^^^  g  j3g  perches. 

TAe  area  o/  a  circle  given,  to  find  the  periphery,  or 

circumference, 

sau^r^f  tL"^  ••  i^^^'  ^''  "^  ^  •  ^2,56637  :  :  the  area  to  the 

Xhv  s^iioP'"i'^r^''~r'  ™"^'^P^^  *^^  «q«^'-^  root  of  the 
area  by  3,5449,  and  the  product  is  the  circumference. 

EXAMPLES. 

30.  When  the  area  is  12,  what  is  the  circumference  ? 

Ans.  12,279. 

31.  When  the  area  is  160,  what  is  the  periphery? 

Ans.  44,839. 
sid^"^  two  sides  of  a  right-angled  triangle  given,  to  find  the  third 

fa^^  „n(i  j^ci^cuuiuuxar  given  lo  nna  the  hypothenuse. 

an?n«f    ^^^  square  root  of  the  sum  of  the,  squares  of  the  base 
and  perpendicular,  is  the  length  of  the  hypothenuse. 


I .' 


134 


BX'ERACTIOTr   OF   THE    SaVJ^E   ROOT. 


/w 


*  EXAMPLES. 

32.  The  top  of  a  castle  from  the  ground  is  45  yards  high,  and 
surrounded  with  a  ditch  60  yards  broad ;  what  length  must  a  lad- 
der be  to  reach  from  the  outside  of  the  ditch  to  the  top  of  the 
castle  ?  -4ws.  75  yards. 


S3 
I 

a 


Ditch. 


a> 

^^ 

■J§ 

o 

, 

CO 

1 

«4-l 

t^ 

o 

«3 

""t 

feD 

a> 

w 

Base  60  yards. 

33.  The  wall  of  a  town  is  25  feet  high,  which  is  surrounded 
by  a  moat  of  30  feet  in  breadth :  I  desire  to  know  the  length  of 
a  ladder  that  will  reach  from  the  outside  of  the  moat  to  the  top 
of  the  wall  ?  -Ans.  39,06  feet. 

The  hypothenuse  and  perpendicular  given,  to  find  the  base. 
Rule.   The  square  root  of  the  difference  of  the  squares  of  the 
hypothenuse  and  perpendicular,  is  the  length  of  the  base. 

The  base  and  hypothenuse  given,  to  find  the  perpendicular. 

Rule.  The  square  root  of  the  difference  of  the  squares  of  the 
hypothenuse  and  base,  is  the  height  of  the  perpendicular. 

N.  B.  The  two  last  questions  may  be  varied  for  examples  to 
the  two  last  propositions. 

Any  number  of  men  being  given,  to  form  them  into  a  square 
battle,  or  to  find  the  number  of  rank  and  file. 

Rule.  The  square  root  of  the  number  of  men  given,  is  the 
number  of  men  either  in  rank  or  file. 

34.  An  army  consisting  of  331776  men,  I  desire  to  know,  how 
ok  and  tile  ?  -Ans.  57G. 
L  certain  square  pavement  contains  48841  squaji-e  stones, 
e  same  size.     I  demand  how  many  are  contained  in  one 


many  r 

ar,. 

all  of  t 

c"  the  sides  ? 


Ans.  221, 


BXTBACTION   OF   THE   CUFE  ROOT. 


1^ 


EXTRACTION  OF  THE  CUBE  ROOT. 

To  extract  the  Cube  Root  is  to  find  out  one  number,  which  be* 
ing  multiplied  into  itself,  and  then  into  that  product,  produceth 
the  given  number. 

Rule.  1.  Point  every  third  figure  of  the  cube  given,  beginning 
at  the  unit's  place ;  seek  the  greatest  cube  to  the  first  point,  and 
subtract  it  therefrom  ;  put  the  root  in  the  quotient,  and  bring  down 
the  figures  in  the  next  point  to  the  remainder,  for  a  Resolvend. 

2.  Find  a  Divisor  by  multiplying  the  square  of  the  quotient 
by  3.  See  how  often  it  is  contained  in  the  resolvend,  rejecting 
the  units  and  tens,  and  put  the  answer  in  the  quotient. 

3.  To  find  the  Subtrahend.  1.  Cube  the  last  figure  in  the 
quotient.  2.  Multiply  all  the  figures  in  Ihe  quotient  by  3,  except 
the  last,  and  that  product  by  the  square  of  the  last.  3.  Multiply 
the  divisor  by  the  last  figure.  Add  these  products  together,  for 
the  subtrahend,  which  subti^t  from  the  resolvend ;  to  the  re- 
mainder bring  down  the  next  point,  and  proceed  as  before. 


Roots. 
Cubes. 


r.  2.    3,    4._,  6.      6.      1.      8.      9. 


li^^ 


1.  8*  2'rr'61E.  J25.  216.  343.  512.  729. 


EXAMPLES. 
1.  What  is  the  cube  root  of  99252847  ? 


99252847(463 
64       =cube  of  4 


Divisor- 


Square  of  4X3=48)35252  resolvend. 


216=cube  of  6. 
432  =4X3Xby  square  of  6. 
288     %divisorXby  6. 


Divisor- 


33336  subtrahend. 


Square  of  46X3=6348)1916847  resolvend. 


,      27=cube  of  3. 
1242=46X3Xby  square  of  3. 
19044     =divisorXby  3. 


1916847  subtrahend. 
M2 


/ 


A 


/ 


186 


EXTRACTION  OP  THE  CUBE  ROOT. 


4 


2.  What  is 
8.  What  is 
4.  What  is 
6.  What  is 
6.  What  is 
1.  What  is 

8.  What  is 

9.  What  is 

10.  What  is 

11.  What  is 

12.  What  is 


the  cube  root  of  389017  ? 
the  cube  root  of  5735339? 
the  cube  root  of  32461759  ? 
the  cube  root  of  84604619  ? 
the  cube  root  of  259694072  ? 
the  cube  root  of  48228544  ? 
the  cube  root  of  27054036008  ? 
the  cube  root  of  22069810125  ? 
the  cube  root  of  122615327232  ? 
the  cube  root  of  219365327791  ? 
the  cube  root  of  673373097125  ? 


Ans.  73. 
Ans.  179. 
Ans.  319. 
Am.  439. 
Ans.  638. 
Ans.  364. 
Ans.  3002. 
Ans.  2805. 
Ans.  4968. 
Ans.  6031. 
Ans.  8765. 


When  the  given  number  consists  of  a  whole  number  and  deci- 
mals together,  make  the  number  of  decimals  to  consist  of  3,  6,  9, 
&c.  places,  by  adding  ciphers  thereto,  so  that  there  may  be  a 
point  fall  on  the  unit's  place  of  the  whole  number. 

13.  What  is  the  cube  root  of  12,f77875  ?  Ans.  2,35. 

14.  What  is  the  cube  root  of  36155,02756  ?     Am.  33,06+. 

15.  What  is  the  cube  root  of  ,001906m.?    .       Ans.  ,124. 

16.  What  is  the  cube  root  of  l^^9fm^4  ?  Am.  3,2164-. 

17.  What  is  the  cube  root  of  15926,972504  ?  Am.  25,16-|-. 

18.  What  is  the  cube  root  of  ,053157376  ?  Ans.  ,376. 

To  extract  the  cube  root  of  a  vulgar  fraction. 

Rule.   Reduce  the  fraction  to  its  lowest  terms,  then  extract 
the  cube  root  of  its  numerator  and  denominator,  for  a  new  nu- 
^  merator  and  denominator ;  but  if  the  fraction  be  st  surd,  reduce 
it  to  a  decimal,  and  then  extract  the  root  from  it  ? 


EXAMPLES. 

19.  What  is  the  cube  root  of  f ff  ? 

20.  What  is  the  cube  root  of  jU^*^  ? 

21.  What  is  the  cube  root  of  -Raa  ? 


Am.  4- 
Ans.  |. 
Ans.  |. 


\ 


SURDS.  .m^ 

22.  What  is  the  cube  root  of  4  ?  Am.  ,829+. 

23.  What  is  the  cube  root  of  ^  ?  Am.  ,822+. 

24.  What  is  the  cube  root  of  |  ?  Am.  ,873+. 

To  extract  the  cube  root  of  a  mixed  number. 
Rule.  Reduce  th^  fractional  part  to  its  lowest  terms,  and  then 
the  mixed  number  to  an  improper  fraction,  extract  the  cube  root 
>f  the  numerator  and  denominator  for  a  new  numerator  and  deno- 


BXTRACTIOrr   OP   THE    CT7BB    ROOT. 


f87 


minator;  but  if  the  mixed  number  given  be  a  surd,  reduce  the 
fractional  part  to  a  decimal,  annex  it  to  the  whole  number,  and 
extract  the  root  therefrom. 

EXAMPLES. 

25.  What  is  the  cube  root  of  12Af  ? 

26.  What  is  the  cube  root  of  31  JJL  ? 
27    What  is  the  cube  root  of  405  A?-  ? 

13  5 


Ans.  2|. 
Ans.  ^. 
Ans.  7|. 


SURDS. 

28.  What  is  the  cube  root  of  1\  ? 

29.  What  is  the  cube  root  of  9|  ? 

30.  What  is  the  cube  root  of  8f  ? 

THE  APPLICATION. 


Am.  1,93+. 
Ans.  2,092-f . 
Ans.  2,0574". 


1-   If  a  cubical  piece  of  timber  be  47  inches  long,  47  inches 
broad,  and  47  mches  deep,  how  many  cubical  inches  doth  it  con- 
^^  •  Ans.  103823 

2.  There  is  a  cellar  dug,  that  is  12  feet  every  way,  in  length, 
breadth,  and  depth;  how  many  sohd  feet  of  earth  were  taken  out 

.  Ans.  1728. 

3.  There  is  a  stone  of  a  cubic  form,  which  contains  389017 
solid  teet,  what  is  the  superficial  content  of  one  of  its  sides  ? 

Ans.  5329. 

Between  two  numbers  given,  to  find  two  mean  proportionals. 

Rule.  Divide  the  greater  extreme  by  the  less,  and  the  cube 
root  of  the  quotient  multiplied  by  the  less  extreme,  gives  the  less 
mean ;  multiply  the  said  cube  root  by  the  less  mean,  and  the  pro- 
duct will  be  the  greater  mean  proportional. 

EXAMPLES. 

4.  What  are  the  two  mean  proportionals  between  6  and  162  ? 

e   TI71   .         1  ■^***-  18  and  64. 

o.  VVhat  are  the  two  mean  proportiQnals  between  4  and  108  ? 

Ans,  12  and  36. 

^  :■  jvrc^z-  wco  ciae  vj  t*  o-«t/c  mai  snau  oe  equal  m  solidity  to  any 
given  solid,  as  a  globe,  cylinder,  prism,  cone,  <Jtc. 

Rule.  The  cube  root  of  the  solid  content  of  any  solid  body 
given,  is  the  side  of  the  cube  of  equal  solidity. 

Md 


188 


EXTRACTING   ROOTS    OP   ALL   POWERS. 


EXAMPLES. 

6.  If  the  solid  content  of  a  globe  is  10648,  what  is  the  side  of 
a  cube  of  equal  solidity  ?  Ans.  22. 

The  side  of  a  cube  being  given,  to  find  the  side  of  a  cube  that 
shall  be  double,  treble,  dc.  in  quantity  to  the  cube  given. 

Rule.  Cube  the  side  given,  and  multiply  it  by  2,  3,  &c.,  the 
cube  root  of  the  product  is  the  side  sought. 

EXAMPLES.  • 

1.  There  is  a  cubical  vessel,  whose  side  is  12  inches,  and  it  is 
required  to  find  the  side  of  another  vessel,  that  is  to  contain  three 
times  as  much  ?  Ans.  17,306. 

EXTRACTING  OF  THE  BIQUADRATE  ROOT. 

To  extract  the  Biquadrate  Root,  is  to  find  out  a  number,  which 
being  involved  four  times  into  itself,  will  produce  the  given  num- 
ber. 

Rule.  First  extract  the  square  root  of  the  given  number,  and 
then  extract  the  square  root  of  that  square  root,  and  it  will  give 
the  biquadrate  root  required. 

EXAMPLES. 

T.  What  is  the  biquadrate  of  27  ?  Ans.  531441. 

2.  What  is  the  biquadrate  ^0Q  ?     *'  Ans.  33362176. 

3.  What  is  the  biquadw^'df  275  ?  Ans.  6719140625. 

4.  What  is  the  biquadrate  root  of  631441  ?  Ans.  27. 
6.  What  is  the  biquadrate  root  of  33362176  ?  Ans.  76. 
6.  What  is.  the  biquadrate  root  of  5719140626  ?       Ans.  276. 

A  GENERAL  RULE  FOR  EXTRACTING  THE  ROOTS 

OF  ALL  POWERS. 

1.  Prepare  the  number  given  for  extraction,  by  pointing  off 
from  the  unit's  place  as  the  root  required  directs. 

2.  Find  the  first  f.gure  in  the  root,  which  subtract  from  the 
^ven  number. 

8.  Bring  down  the  first  figure  in  the  next  point  to  the  remain- 
der, and  call  it  the  dividend. 


EXTBACTING   BOOTS   OP    ALL    POWERS.  139 

^    4.  Involve  the  root  into  the  next  inferior  power  to  that  which 

18  given    multiply  it  by  the  given  power,  and  call  it  the  divisor 

6.  Find  a  quotient  hgure  by  common  division,  and  annex  it  tj 

^"i  TA^eZZtZ!"'  "'^^^  ^^^^  ""^ '''  ^''-'^  1--'  -^ 

6.  Subtract  that  number  from  as  many  points  of  the  ffiven 
power  as  are  brought  down,  beginning  at  the  lower  place,  and 
to  the  remainder  bring  down  the  first  figure  of  the  next  point  for 
a  new  dividend.  ^ 

V.  Find  a^ew  divisor,  and  proceed  in  all  respects  as  before. 

'  EXAMPLES. 
1.  What  is  the  square  root  of  1413V6  ? 


141376(376 
9 

6)51  dividend. 

1369  subtrahend. 


3X     2=6  divisor. 
37  X   37=1369  subtrahend. 
37x     2=74  divisor. 
376X376=141376  subtrahend. 


74)447  dividend. 


141376  subtrahend. 
2.  What  is  the  cube  root  of  63157376  ? 


63157376(376 


27 


E  ROOTS 


27)261  dividend. 
60653  subtrahend. 


4107)25043  dividend. 
53157376  subtrahend. 


3X     3X     3=27  divisor. 
37x   37x   37=50653  subtrahend. 
37x   37x     3  =  4107  divisor. 
376X376X376=53157376  subtrahend. 


140  SIMPLE    INTEBB8T. 

3.  What  is  the  biquadrate  of  199Bll1d3lQ  ? 

19987173376(376 
81 


.*: 


108)1188  dividend. 
1874161  subtrahend. 


202612)1246563  dividend. 


19987173376  subtrahend. 


3X      3X     3X     4=108  divisor. 
37x   37X   87X   37=1874161  subtrahend. 
37  X   37  X   37  X     4=202612  divisor. 
376X376X376X376=19987173376  subtrahend. 

SIMPLE  INTEREST. 

There  are  five  letters  to  be  observed  in  Simple  Interest,  viz. 

P.  the  Principal. 

T.  the  Time. 

R.  the  Ratio,  or  rate  per  cent. 

I.   the  Interest. 

A.  the  Amount. 


s\ 


A  TABLE  OF  RATIOS 


3 

,03 

5i 

,055 

8 

,08 

3^ 

,035 

6 

,06 

8i 

,085 

4 

,04 

H 

,065 

9 

,09 

^ 

,045 

7 

,07 

H 

,095 

5 

,05 

n 

,075 

10 

,1 

the  rate  per  cent,  proposed,  and  is  found  thus 


of 


£     £     £ 
As  200  ;  3  :  :  1  :  ,03 


As  100  :  3,5  :  :  1  :  ,036. 


8IMPLE    INTEREST. 


141 


,08 

,085 

,09 

,095 

,1 

of 

1    «v 

When  the  principal,  Unhand  rate  per  cent,  are  given,  to  find 

the  interest.  #  *^ 

wift  tSL^^eVCr '■ '-.  -<!  -te  together,  and  it 
Rule.  prt=I. 

EXAMPLES. 

1.  What  is  the  interest  of  £94.5  •  in  f^^  o 
per  annum.     ^«.  945,SX  OsTs-wl  fj  ^T,'.",'  ^  P''  "*"'• 

2    What  is  the  mterit  of  £?47~  f  f  4' "  f "  ^  "  ^  «• 
for  6  years  ?  j       J,  „  *  P"^!^  eent.  per  annum, 

3.  What  is  the  interest  of  £796    I5  j  ''A  =  "'  ^  "l"^-  '"«• 
num,  for  5  years?  "      '  ?'  *i  P^""  "^nt-  Per  an- 

4.  What  is  the  interest  of  £397  •  9  4lrTx  '  ^  =  *  ?  .T" 
cent,  per  annum  ?  L,  f^:     .  ^  ^'""'^'  "*  ^i  F' 

6.  What  is  the  interest  of  £557  \lt  V     ,=  '^  ^'"®*  *>■*• 
at  4i  per  cent,  per  annum"  '       '  "/"''  L^'f^'^  «  """'h^- 

0.    What  is  L  in.«"st  of  £236  •  18     S^'Vfr  V  "  =  '  '' 
months,  at  5i  per  cent,  per  annumf  Z  £«'ri5 YTi  '293'  ' 

^<^  Ike  interest  is  for  any  number  0/ days  miv.' 
INTEREST  OF  £1  FOR  ONE  DAY. 


Decimals. 
,00008219178 
,00009589041 
,00010958904 
,00012328767 
,00013698630 
,00015068493 


per  cent. 
6i 

7 

8 
9 

r\  1 


Decimals. 
,00017808219 
,00019178082 
,00020547945 
,00021917808 
,00023287671 
,00024657534 
,00026027397 


Note.  The  above  table  is  thus  found  :— 

As  365  :  ,03  :  :  1  :  ,00008219178.  And  as  365  :  ,086  •  •  1 

,00009589041,  (fee.        ^     o..i 


142 


SIMPLE    INTEREST. 


EXAMPLES. 

I.  What  is  the  interest  of  £240,  for  120  days,  at  4  per  cent, 
per  annum  \        Ans.  ,00010958904  X  240  Xl20=£3  :  3t  1^. 

8.  What  is  the  interest  of  £364  :  18,  for  154  days,  at  5  per 
cent,  per  annum?  Ans.  £7  :  13  :  11  J. 

9.  What  is  the  interest  of  £725  :  16,  for  74  days,  at  4  per  cent, 
per  annum?  Ans.  £5  :  17  :  8^. 

10.  What  is  the  interest  of  £100,  from  the  1st  of  June,  1775, 
to  the  9th  of  March  following,  at  5  per  cent,  per  annum  ? 

Ans.  £3  :  16  :  llf. 

II.  When  P  R  T  are  ffiven  to  find  A. 


Rule,  prt  +  p=A. 


EXAMPLES. 


11.  What  will  £279  ;  12,  amount  to  in  7  years,  at  4^  per  cent, 
per  annum  ?  Ans.  £367  :  13  :  5  3,04  qrs. 

279,6  X  ,045  X  7  +  279,6=367,674. 

12.  What  will  £320  :  17,  amount  to  in  5  years,  at  3^  per  cent, 
per  annum?  Ans.  £376  :  19  :  11  2,8  qrs. 

When  there  is  any  odd  time  given  with  the  whole  years,  reduce 
the  odd  time  into  days,  and  work  with  the  decimal  parts  of  a 
year  which  are  equal  to  those  days. 

13.  What  will  £926  :  12,  amount  to  in  5^  years,  at  4  per  cent, 
per  annum?  Ans.  £1130  :  9  :  0^  ,92  qrs. 

14.  What  will  £273  :  18,  amount  to  in  4  years,  175  days,  at  3 
per  cent,  per  annum?  Ans.  £310  :  14  :  1  3,35080064  qrs. 

in.  When  A  R  T  are  given  to  find  P. 

a 
Rule. =P. 


rt,+  1. 


EXAMPLES. 


^ 


15.  What  principal,  being  put  to  interest,  will  amount  to  £36 
13  :  5  3.04  ora.  in  7  vears.  at  4*  ner  cent.  Der  annum  ? 

Ans.  ,045X''7+1=1,315  then'367,674-rl,315=£279  :  12. 

16.  What  principal,  being  gut  to  interest,  will  amount  to  £376 
19  :  11  2,8  in  5  years,  at  S^'per  cent,  per  annum? 

Ans.  £320  :  17. 


SIMPLE    INTEREST. 


143 


i 


11.   What  principal,  being  put  to  interest,  will   amount  to 
£1130  :  9  :  0^  ,92  qrs.  in  5|  years,  at  4  per  cent,  per  annum  ? 

Ans.  £026  :  12. 

18.  5Vhat  principal  will  amount  to  £310  :  14  :  1  3,35080064 
qrs.  in  4  years,  175  days,  at  3  per  cent,  per  annum? 

Ans.  £273  :  18. 

IV.  When  A  P  T  are  given  to  find  R.  ♦ 

a — p 

Rule. ==R. 

pt 

EXAMPLES. 

19.  At  what  rate  per  cent,  will  £279  :  12,  amount  to  £367  : 

13  :  5  3,04  qrs.  in  7  years? 

Ans.  367,674—279,6  =  88,074,  275,6x7=1957,2, 
then  88,074-M957,2=,045  or  4^  j^er  cent. 

20.  At  what  rate  per  cent,  will  £320  :  17,  amount  to  £376 
19  ;  11  2,8  qrs.  in  5  years?  ^       Ans.  3^  per  cent. 

21.  At  what  rate  per  cent,  will  £926  :*12,  amount  to  £1130 
9  :  0^  ,92  qrs.  in  5^  years  ?  Ans.  4  per  cent. 

22.  At  what  rate  per  cent,  will  £273  :  18,  amount  to  £310 

14  :  1  3,35080064  qi-s.  in  4  years,  175  days? 

Ans.  3  per  cent. 

V.  When  A  P  R  are  given  to  find  T. 

a — p 

Rule. =T. 

pr. 

EXAMPLES. 

23.  In  what  time  will  £279  :  12,  amount  to  £367  :  13  :  5  3,04 
qrs.  at  4^  per  cent.  ? 

Ans.  367,674—279,6=88,074.  279,6X  ,045=12,5820,  then 
88,074-f- 12,5820=7  years.  4 

24.  In  what  time  will  £320  :  17,  amount  to  370  :  19  :  11  2,8 
qra.  at  3^  per  cent.  ?  Ans.  5  years. 

25.  In  what  time  will  £926  :  12,  amount  to  £1130  :  9  :  0|- 
,92  qrs.  at  4  per  cent.  ?  Ans.  5|  years. 

26.  In  what  time  will  £273  :  18,  amount  to  £310  :  14  :  1 
3,35080064  qi-s.  at  3  per  cent.  ?  Ans.  4  years,  175  days. 

ANNTTTTTFS  OR   Pr<!lVSTn\ra    Arr^    TM    ARRPAPS 

Annuities 


pensions, 


to 


are  payable  or  due,  cither  j'oarly,  half-yearly,  or   qunrtorly,  aiul 
are  unpaid  for  any  number  of  ]"»aymont?. 


14-1 


SIMPLE    IMTEHEST. 


Note.    U  represents  the  annuity,  pension,  or  yearly  rent,  T 
B  A  as  before. 

I  U  R  T  are  given  to  find  A 

ttu — tu  ^ 

Rule. X  r:  +tu=A. 


EXAMPLES. 

27.  If  a  salary  of  £150  be  forborne  6  years  at  5  per  cent,  what 
will  it  amount  to  ?  Arts,  £826. 
3000 

6X 5 X 150—5 X  150=3000 then X  ,06+5 X  150=£825. 

2 

28.  If  £250  yearly  pension  be  forborne  Y  years,  what  will  it 
amount  to  in  that  time  at  6  per  cent.  ?  •      Ans.  £2065. 

29.  There  is  a  house  let  upon  lease  for  5^  years,  at  £60  per 
annum,  what  will  be  the  amount  of  the  whole  time  at  4^  per 
cent.  ?  •  Ans.  £363  :  8  :  3. 

30.  Suppose  an  annual  pension  of  £28  remain  unpaid  for  8 
years,  what  would  it  amount  to  at  5  per  cent.  ? 

Ans.  £263  :  4. 
Note.  When  the  annuities,  &c.  are  to  be  paid  half-yearly  or 
quarterly,  then 

For  half-yearly  payments,  take  half  of  the  ratio,  half  of  the 
annuity,  &c.,  and  twice  the  number  of  years — and 

For  quarterly  payments,  take  a  fourth  part  of  the  ratio,  a  fourth 
part  of  the  annuity,  <fec.,  and  four  times  the  number  of  years, 
and  work  as  before. 

EXAMPLES. 

31.  If  a  salary  of  £150,  payable  every  half-year,  remains  un- 
paid for  5  years,  what  will  it  amount  to  in  that  time  at  5  per 
cent.  ?  Ans.  £834  :  7  :  6. 

32.  If  a  salary  of  £150,  payable  every  quarter,  was  left  unpaid 
for  5  years,  what  would  it  amount  to  in  that  time  at  5  per  cent.  ? 

Ans.  £839  :  1  :  3./ 
Note.   It  may  be  observed  by  comparing  these  last  examples, 
the  amount  of  the  half-yearly  payments  are  more  advantageous 
than  the  yearly,  and  the  quarterly  more  than  the  half-yearly. 
IT,  When  A  R  T  are  oiven  to  find  U» 


2a 


RULE.- 


=u. 


ttr— tr-f-2t 


«I1IPLE  INTBBB8T. 


145 


33.  If  a  salary  amounted  to  £825  in  fivo  years,  at  5  per  cent, 
what  was  the  salary  ?  ''        Am  £\^Q 

825X2=1650  5X5X,05-5X,05+5X2=11  then  1650-^ 

11  =£150. 

34.  If  a  house  is  to  be  let  upon  a  lease  for  5^  years,  and  the 
jrry  ren[?     ' ''""  "  ^'''  :  S  :  3,  at  4^  per  cU.  what  is  the 

*K^f*  ^^  f,  P^"^^«?  amounted  to  £2065,  in  7  years,  at  6^  per  cent. 
Krhat  was  the  pension  ?  ^  Am  260 

^  36.  Suppose  the  amount  of  a  pension  be  £263  :  4  in  8  years'  at 

0  per  cent,  what  was  the  pension  ?  Ans,  £2H, 

Note  When  the  payments  are  half-yearly,  then  take  4  a,  and 
halt  of  the  ratio,  and  twice  the  number  of  years ;  and  if  quarterly 
then  take  8  a,  one  fourth  of  the  ratio,  and  four  times  the  number 
ot  years,  and  proceed  as  before. 

37.  If  the  amount  of  a  salary,  payable  half-yearly,  for  5  years 

d8.  It  the  amount  of  an  annuity,  payable  quarterly,  be  £839  : 

1  :  3,  tor  o  years,  at  6  per  cent,  what  was  the  annuity  ? 

Ans.£\bO. 

m.  When  U  A  T  are  given  to  find  R. 

2a— 2ut 
Rule. =R, 


utt — ut 


EXAMPLES. 


39.  If  a  salaiy  of  £150  per  annum,  amount  to  iB825,  in  5  years, 
what  13  the  rate  per  cent.  ?  Arts,  5  per  cent 

T 150 

825+2— 150-^-5+2=:  150  then =,05 

150X5X5—150X5 

40.  If  a  house  be  let  upon  a  lease  for  ^  years,  at  £60  per  an- 
n«m,  and  the  amount  for  that  time  be  £363  :  8  :  3,  what  is  the 
rate  per  cent.?  ^r...  4^  per  cent. 

II  a  pension  of  £250  per  annum,  amounts  to  £2005  in  V 

VVhnf    1G     fl^rt     r^n^rx     -^r^^     ^^^*.       (1  A  ^  . 


4   t 


yojirs,  what  is  the  rate  per  cent.  ? 


Ans.  6  per  cent. 


4J.  feuppose  the  amount  of  a  yearly  pension  of  £28,  be  £263  : 
4,  m  8  years,  what  is  the  rate  per  cent.  ?  Ans.  5  per  cent. 

N 


146 


BIMPLB    INTEREST. 


Note.  When  the  payments  are  half-yearly,  take  4  a— 4  ut  for 
:i  dividend,  and  work  with  half  the  annuity,  and  double  the  num- 
i>or  of  years  for  a  divisor  ;  if  quarterly,  take  8  a— 8  ut,  and  work 
with  a  fourth  of  the  annuity,  and  four  times  the  number  of  years. 

43.  If  a  salary  of  £150  per  annum,  payable  half-yearly, 
amounts  to  £834  :  7  :  6,  in  5  years,  what  is  the  rate  per  cent.  ? 

Ans.  5  per  cent. 

44.  If  an  annuity  of  £150  per  annum,  payable  quarterly, 
amounts  to  £839  :  1  :  3,  in  6  years,  what  is  the  rate  per  cent.  ? 

Ans.  5  per  cent. 
IV.   When  U  A  R  are  given  to  find  T. 


=T. 


2  2a     XX 

Rule.   First, 1 =x  then :  ^ [ 

r  ur       4       2 

EXAMPLES. 

45.  In  what  time  will  a  salary  of  £150  per  annum,  amount  to 
£825,  at  5  per  cent.  ?  Ans.  5  years. 
2                   826X2                39X39 
1=39 =  220 =380,26 


,05 


160  X, 05 


4 
39 


v/220-f  380  ,25=24  ,5 =5  years. 

2 


40.  If  a  house  is  let  upon  a  lease*  for  a  certain  time,  for  £60 
per  annum,  and  amounts  to  £363  :  8  :  3,  at  4J  per  cent.,  what 
time  was  it  let  for  ?  Ans.  5^  years. 

47.  If  a  pension  of  £250  per  annum,  being  forborne  a  certain 
time,  amounts  to  £2065,  at  6  per  cent.,  what  was  the  time  of 
forbearance  ?  "  Ans.  1  years. 

48.  In  what  time  will  a  yearly  pension  of  £28,  amount  to 
£263  :  4,  at  5  per  cent.  ?        '  Ans.  8  years. 

Note.  If  the  payments  are  half-yearly,  take  half  the  ratio,  and 
half  the  annuity;  if  quarterly,  one  fourth  of  the  ratio,  and  one 
fourth  of  the  annuity ;  and  T  will  be  equal  to  those  half-yearly 


or  niM\vfnr\\T  •nQXTmnnl-o 


49.  If  an  annuity  of  £150  per  annum,  payable  half-yearly, 
amounts  to  £834  :  7  :  6,  at  5  per  cent.,  what  time  was  the  pay- 
ment forborae  ?  A71S.  5  years. " 


SIMPLE    INTEREST. 


147 


J2;  ^1  ^  yearly  pension  of  £150,  payable  quarterly,  amounts  to 
AB3y  .  1  :  3,  at  6  per  cent.,  what  was  the  time  of  forbearance? 

Ans.  6  years. 

PRESENT  WORTH  OF  ANNUITIES. 

Note.  P  represents  the  present  worth ;  U  T  R  as  before. 

I.  When  U  T  R  are  given  to  find  P. 

ttr— tr  +  2t 
Rule. :  x  u=P. 


2tr  +  2 


EXAMPLES. 


.61.  What  is  the  present  worth  of  £150  per  annum,  to  continue 
5  years  at  5  per  cent,  'i  J^^^  ^gg^^ 

5X5x;05l-5x, 05+5X2^11 ,5  X  ,05X2+2=2,6  then  11-^ 

2,5X150=£660. 

52.  What  is  the  yearly  rent  of  a  house  of  £60,  to  continue  5* 
years  worth  m  ready  money,  at  4  J  per  cent.  ? 

Ko   wu  .  •   .1.  ,  •^^*-  ^291  :  6  :  3. 

53.  What  IS  the  present  worth  of  £250  per  annum,  to  continue 

IT'^^t  ^  P''  '^'"^'  •  ^^''  ^1454  :  4  :  6. 

.54.  What  IS  a  pension  of  £28  per  annum,  worth  in  ready  mo- 
ney, at  5  per  cent,  for  8  years  ?  Ans.  £l  88. 

Note.  The  same  thing  is  to  be  observed  as  in  the  first  rule  of 
annuities   m   arrears,  concerning   half-yearly  and   quarterly  pay- 

65.  What  is  the  present  worth  of  £150,  payable  quarterly,  for 
5  years,  at  5  per  cent.  ?  Ans.  £611  :  5i 

Note.  By  comparing  the  last  examples,  it  will  be  found  that 
the  present  worth  of  half-yearly  payments  is  more  advantageous 
than  yearly,  and  quarterly  than  half-yearly. 

II.  When  P  T  R  are  given  to  find  U. 


Rule.— 


tr-f  1 


ttr— tr  +  2t 


X  2p=U. 


^9 


148 


SIMPLE   INTERB8T. 
EXAMPLES. 


56.  If  the  present  worth  of  a  salary  he  £660,  to  continue  5 
years,  at  5  cent.,  what  is  the  salary?  Ans.  £150. 

6X  ,05+1  =  1,25  5  X  5  X  ,05—5  X  ,05  +  10  =  11. 

1,25 

X  660  X  2  =  £150. 

11 

67.  There  is  a  house  let  upon  lease  for  5^  years  to  come,  I  de- 
sire to  know  the  yearly  rent,  when  the  present  worth,  at  4^  per 
cent,  is  £291  :  6  :  3  ?  Ans.  £60. 

58.  What  annuity  is  that  which,  for  1  years'  continuance,  at  6 
per  cent.,  produces  £1454  :  4  :  6  present  worth?       Ans.  £250. 

59.  What  annuity  is  that  which,  for  8  years'  continuance,  pro- 
duces £188  for  the  present  worth,  at  5  per  cent.  ?        Ans.  £28. 

Note.  When  the  payments  are  half-yearly,  take  half  the  ratio, 
twice  the  number  of  years,  and  multiply  by  4  p ;  and  when  quar- 
terly, take  one  fourth  of  the  ratio,  and  four  times  the  number  of 
years,  and  multiply  by  8  p. 

60.  There  is  an  annuity  payable  half-yearly,  for  5  years  to 
come,  what  is  the  yearly  rent,  when  the  present  worth,  at  5  per 
cent.,  is  £667  :  10  ?  Ans.  £150. 

61.  There  is  an  annuity  payable  quarterly,  for  5  years  to  come, 
I  desire  to  know  the  yearly  income,  when  the  present  worth,  at 
5  per  cent.,  is  £671  :  5  ?  Ans.  £150. 

III.  When  U  P  T  are  given  to  find  R. 


R^tE.- 


ut— p  X  2 


=R. 


2pt  +  ut — ^ttu 


EXAMPLES. 


62.  At  what  rate  per  cent,  will  an  annuity  of  £150  per  annum, 
to  continue  5  years,  produce  the  present  worth  of  £660  ? 

Ans.  5  per  cent. 


150X5-660X2  =  180,2X660X5  +  5X150-5X5X150=3600 
then  i80-^3600:=:,05=5  per  eont. 

63.  If  a  yearly  rent  of  £60  per  annum,  to  continue  Bl  yoars, 
produces  £291  :  6  :  3,  for  the  present  worth,  what  i^  the  rale 
per  cent.  ?  Ans.  4^  per  cent. 


SIMPLE    INTBRBBT. 


JNv 


64.  If  an  annuity  of  £250  per  annum,  to  continue  1  yeai-s, 
produces  £1454  :  4  :  6,  for  the  present  worth,  what  is  the  rate 
per  cent.  ?  ji^s.  6  per  cent. 

65.  If  a  pension  of  £28  per  annum,  to  continue  8  years,  pro 
duces  £188  for  the  present  worth,  what  is  the  rate  per  cent.  ? 

Ans,  5  per  cent. 

Note.  When  the  annuities,  or  rents,  &c.  are  to  be  paid  half- 
yearly,  or  quarterly,  then 

For  half-yearly  payments,  take  half  of  the  annuity,  &c.  and 
twice  the  number  of  years,  the  (quotient  will  be  the  ratio  of  half 
the  rate  per  cent. — and 

For  quarterly  payments,  take  a  fourth  part  of  the  annuity,  &c. 
and  four  times  the  number  of  years,  the  quotient  will  be  the  ratio 
of  the  fourth  part  of  the  rate  per  cent. 

^  66.  if  an  annuity  of  £150  per  annum,  payable  half-yearly,  ha- 
ving 5  years  to  come,  is  sold  for  £667  :  10,  what  is  the  rate  per 
^^^^-  ^  Ans.  5  per  cent. 

^  67.  If  an  annuity  of  £150  per  annum,  payable  quarterly,  ha- 
ving 5  years  to  come,  is  sold  for  £671  :  5,  what  is  the  rate  per 
^^^^'  •  Ans.  5  per  cent 

IV.  When  U  P  R  are  given  to  find  T. 

2       2p  *        •  2p     xlc      X 

Rule. 1  =x  then  ^ — | =T. 

t        n  ur      4       2 


r  annum, 


EXAMPLES. 

68.  If  an  annuity  of  £150  per  annum,  produces  £660  for  the 
present  worth,  at  5  per  cent.,  what  is  the  time  of  its  continu- 
ance? ^ws.  6  years. 


660X2 


,05    ■  150 

30,2X30,2 


—1=30,2 


660X2 

=176 

150  X, 05 


=228,01  then  ^/228j01-f-176— 20,1 


30,2 


20,1- 


=5  years. 


y/i 


150 


SIMPLE    INTEREST. 


69.  For  what  time  may  a  salary  of  £60  be  purchased  for 
£291  :  6  :  3,  at  4^  per  cent.  ?  Ans.  5^  yeare. 

70.  For  what  time  may  £250  per  annum,  be  purchased  for 
£1454  :  4  :  6,  at  6  per  cent.?  Ans.  1  years. 

71.  For  what  time  may  a  pension  of  £28  per  annum,  be  pur- 
chased for  £188,  at  5  per  cent.  ?  Ans.  8  years. 

Note.  When  the  payments  are  half-yearly,  then  U  will  be 
equal  to  half  the  annuity,  &e.  R  half  the  ratio,  and  T  the  num- 
ber of  payments :  and, 

When  the  payments  are  quarterly,  U  will  be  equal  to  one 
fourth  part  of  the  annuity,  &c.  R  the  fourth  of  the  ratio,  and  T 
the  number  of  payments. 

12.  If  an  annuity  of  £150  per  annum,  payable  half-yearly,  is 
sold  for  £607  :  10,  at  5  per  cent.,  I  desire  to  know  the  number 
of  payments,  and  the  time  to  come  ? 

Ans.  10  payments,  5  years. 

73.  An  annuity  of  £150  per  annum,  payable  quarterly,  is  sold 
for  £671  :  5,  at  6  per  cent.,  what  is  the  number  of  payments,  and 
time  to  come  ?  -y  Ans.  20  payments,  5  years. 

ANNUITIES,  &c.  TAKEN  IN  REVERSION. 

1.  To  find  the  present  worth  of  an  annuity,  &c.  taken  in  re- 
version. 

Rule.    Find  the  present  worth  of  t^e     ttr — tr+2t 


yearly  sum  at  the  given  rate  and  for  the 
time  of  its  continuance ;  -thus, 

2.  Change  P  into  A,  and  find  what  prin- 
cipal, being  put  to  interest,  will  amount  to 
A  at  the  same  rate,  and  for  the  time  to 
come  before  the  annuity  &c.  commences ; 
thus, 

EXAMPLES. 


2tr4-2 


:  X  u=P. 


a 


=P. 


tr-fl 


74.  What  is  the  present  worth  of  an  annuity  of  £150  per  an- 
num, to  continue  5  years,  but  not  to  commence  till  the  end  of  4 
years,  allowing  5  per  cent,  to  the  purcliaser  ?  Ans.  iE550. 


=650. 


6  X, 05X2+2 


4X,05-fl 


SIMPLE    INTEREST. 


151 


15.  What  is  the  present  worth  of  a  lease  of  £50  per  annum, 
to  continue  4  years,  but  which  is  not  to  commence  till  the  end 
of  5  years,  alloAving  4  per  cent,  to  the  purchaser? 

An6'.  £152  :  5  :  11  3  qrs. 

16.  A  person  having  the  promise  of  a  pension  of  £20  per  an- 
nunri,  for  8  years,  but  not  to  commence  till  the  end  of  4  years,  is 
willing  to  dispose  of  the  same  at  5  per  cent.,  what  will  be  the 
present  worth?  Ans.  £111  :  18  :  1  ,14  +  . 

77.  A  legacy  of  £40  per  annum  being  left  for  6  years,  to  a 
person  of  15  years  of  age,  but  which  is  not  to  commence  till  he 
is  21 ;  he,  wanting  money,  is  desirous  of  selling  the  same  at  4 
per  cent.,  what  is  the  present  worth  ? 

Ans.  £171  :  13  :  11  ,07596. 


2.  To  find  the  yearly  income  of  an  annuity,  &c.  in  revei*sion. 

ptr-}-p=A. 


Rule  1.  Find  the  amount  of  the  present 
worth  at  the  given  rate,  and  for  the  time 
before  the  reversion ;  thus, 

2.  Change  A  into  P,  and  find  what  an- 
nuity being  sold,  will  produce  P  at  the 
same  rate,  and  for  the  time  of  its  continu- 
ance; thus, 


tr+1 


ttr— tr+2t 


:X2p=U. 


EXAMPLES. 

78.  A  person  having  an  annuity  left  him. for  5  years,  which 
does  not  commence  till  the  end  of  4  years,  disposed  of  it  for  £550, 
allowing  5  per  cent,  to  the  purchaser,  what  was  the  yearly  m- 
come?  .  ^W5.  £150. 


5  X  ,05  +  1, 


550  X  4  X  ,05  +  550  =  660  5  X  5  X  ,05—5  X  ,05  +  5  X  2= 
,113636  X  660  X  2  =  £150. 

79.  There  is  a  lease  of  a  house  taken  for  4  years,  but  not  to 
commehce  till  the  end  of  5  years,  the  lessee  would  sell  the  same 
for  £152  :  6,  present  payment,  allowing  4  per  cent,  to  the  pur- 
chaser, what  is  the  yearly  rent  ?  Ans.  £50. 

80.  A  person  having  the  promise  of  a  pension  for  8  years, 
which  does  not  commence  till  the  end  of  4  years,  has  disposed  of 
the  same  for  £111  :  18  :  1  ,14  present  money,  allowing  5  per 
cent,  to  the  purchaser,  what  was  the  pension  ?  Ans,  £20. 


152 


BEBATB    OB    DISCOUNT. 


81.  There  is  a  certain  legacy  left  to  a  person  of  15  years  of  age, 
which  is  to  be  contiriued  for  6  years,  but  not  to  commence  till  he 
arrives  at  the  age  of  21 ;  he,  wanting  a  sura  of  money,  sells  it  for 
XI 71  :  14,  allowing  4  per  cent,  to  the  buyer,  what  was  the  an- 
nuity left  him  ?  Ans.  £40. 

REBATE  OR  DISCOUNT. 

Note.  S  represents  the  Sum  to  be  discounted. 
P  the  Present  worth. 
T  the  Time. 
R  the  Ratio. 

I.  When  S  T  R  are  given  to  find  P. 


RULE.- 


tr+1 


■=P. 


EXAMPLES. 

1.  What  is  the  present  worth  of  £357  :  10,  to  be  paid  9  months 
hence,  at  5  per  cent.?  Ans.  £344  :  11  :  6^  ,168. 

2.  What  is  the  present  worth  of  £275  :  10,  due  7  months 
hence,  at  5  per  cent.  I  '     Ans.  £267  :  13  :  lO-i^ij. 

3.  What  is  the  present  worth  of  £875  :  5  :  6,  due  at  5  months 
hence,  at  4|  per  cent.  ?  Ans.  £859  :  3  :  3f  ylg. 

4.  How  much  ready  money  can  I  receive  for  a  note  of  £75, 
due  16  months  hence,  at  5  per  cent.  ? 

Ans.  £70  :  11  :  9  ,l764d. 
II.  When  P  T  R  are  given  to  find  S. 

Rule.  ptr-t-p=S. 

EXAMPLES. 

5.  If  the  present  worth  of  a  sum  of  money,  due  9  months 
hence,  allowing  5  per  cent.,  be  £344  :  11  :  6  3,168  qrs.,  what 
Avas  the  sum  first  due?  Ans.  £B57  :  10. 

344,5783 X  ,75 X  ,05-f  344,5783=£357  :  10. 

6.  A  person  owing  a  certain  sura,  payable  7  months  henoe, 
agiees  with  the  eieditor  to  pay  him  down  £267  :  13  :  lO/y^,  al- 
lowing 6  per  cent,  for  present  payment,  what  is  the  debt  ? 

Ans.  £275  :  10. 

7.  A  person  receives  £869  :  3  :  3|y|j  for  a  sum  of  money 


BBBATE   OR   DIBGOUNTi 


153 


due  8  months  hence,  allowing  the  debtor  4i  per  cent,  for  present 
payment,  what  was  the  sum  due?  Ans  £875  •  5  •  6 

8.  A  person  paid  £70  :  II  :  9  ,1764d.  for'  a  debt  due  *15 
months  hence,  he  bemg  allowed  6  per  cent,  for  the  discount,  how 
much  was  the  debt  ?  ^^  £^g 

III.  When  S  P  T  are  given  to  find  R. 

s — p 
Rule.- =R. 


tp 


examples: 


9.  At  what  rate  per  cent,  will  £367  :  10,  payable  7  months 
hence,  prpduce  £344  :  11  :  6  3,168  qi«s.  for  present  payment? 

3575,-344,5783 

■  — -=,05=5  per  cent. 

344,5783 X  ,75 

10.  At  what  rate  per  cent,  will  £275  :  10,  payable  7  months 
hence,  produce  £267  :  13  :  lO^jV  for  the  present  payment? 

11     Ax     I-  ^     .  ^'^*"  ^  P^^  cent. 

11.  At  what  rate  per  cent,  will  £875  :  5  :  6,  payable  5  months 
lience,  produce  the  present  payment  of  £859  :  3  :  3f  -a_  ? 

io    A 4.     1    X  ■^^*-  "^i  percent. 

12.  At  what  rate  per  cent,  will  £75,  payable  15  months  hence, 
produce  the  present  payment  of  £70  :  11  :  9  ,l764d.  ? 

Ans.  5  per  cent. 
rV.  When  S  P  R  are  given  to  find  T. 

s— p 
Rule.- =T. 


rp 


EXAMPLES. 


13.  The  present  worth  of  ^£357  :  10,  due  at  a  certain  time  to 
come,  IS  £344  :  11  :  6  3,168  qrs.  at  6  per  cent.,  in  what  time 
should  the  sum  have  been  paid  without  any  rebate  ? 

Ans.  9  months, 
357,5—344,6783 

=,75=9  months. 

344,5783  X  ,06 

14.  The  present  worth  of  £275  :  10,  due  at  a  certain  time  to 


154 


EaUATION    OF   PAYMENTS. 


I 


come,  is  £267  :  13  :  10^^'  a^ 
the  sum  have  been  paid  without 

15.  A  person  receives  £859 
Uu'  a  certain  time  to  come, 
de^.'-e  to  knew  in  what  time  the 
ec'  without  any  rebate?  • 

16.  I  have  received  £70  :  1 
allowing  the  person  5  per  cent, 
know  when  the  debt  would  have 


5  per  cent.,  in  what  time  should 

any  rebate  ? 

Ans.  1  months. 

:  3  :  3|  ,0184,  for  £875  :  5  :  6, 

allowing  4|  per  cent,  discount,  I 

debt  should  have  been  discharg- 
ers. 5  months. 

1  :  9,l764d.  for  a  debt  of  £75, 
for  prompt  payment,  I  desire  to 

been  payable  without  the  rebate  ? 
Ans.  15  months. 


EQUATION  OF  PAYMENTS. 

To  find  the  equated  time  for  the  payment  of  a  sum  of  money 
due  at  several  times. 

Rule.  Find  the  present  worth  of  each  pay- 
ment for  its  respective  time ;  thus, 

Add  all  the  present  worths  together,  then, 


s 


tr+1 
s — p=D. 
d 

and =E 

pr 
EXAMPLES. 

1.  D  owes  E  £200,  whereof  £40  is  to  be  paid  at  three  months, 
£60  at  six  months,  and  £100  at  nine  months;  at  what  time  may 
the  whole  debt  be  paid  together,  rebate  being  made  at  5  per  cent.  ? 

Ans.  6  months,  26  days. 

40                        60                         100 
=39,5061 =58,5365 =96,3855 


1,025 


1,0375 


1,0125 

then  200— 39,5061  +  58,5365  +  96,3855=5,5719 

6,6719 

— =,57315=6  months,  26  days. 


194,4281  X  ,05. 

2.  D  owes  E  £800,' whereof  £200  is  to  bo  paid  in  3  months, 

£200  at  4  months,  and  £400  at  6  months ;  but  they,  agieeiug  W 

make  but  one  payment  of  the  whole,  at  the  rate  of  5  per  cent. 

rebate,  the  true  equated  time  is  demanded  ? 

Ans.  4  months,  22  days. 


COMPOUND   INTEREST. 


155 


3.  E  owes  F  £1200,  which  is  to  be  paid  as  follows :  £200 
down,  £500  at  the  end  of  10  months,  and  the  rest  at  the  end  of 
20  months  ;  but  they,  agreeing  to  have  one  payment  of  the  whole, 
rebate  at  3  per  cent.,  the  true  equated  time  is  demanded  ? 

Ans.  1  year,  11  days. 

COMPOUND  INTEREST. 

The  letters  made  use  of  in  Compound  Interest,  are, 

A  the  Amount. 
P  the  Principal. 
T  the  Time. 

R  the  Amount  of  £l  for  1  year  at  any  given  rate  ; 
which  is  thus  found  : 

As  100  :  105  :  :  1  :  1,05.     As  100  :  105,5  :  :  1  :  1,055. 
A  Table  of  the  amount  of  £l  for  one  year. 


RATES 

AMOUNTS 

RATES 

AMOUNTS 

RATES 

AMOUNTS 

PKtt    CENT. 

OF  £1. 

PKR    CENT. 

OF  £1. 

PER    CENT. 

OF    £1 

3 

1,03    • 

5i 

1,035 

8 

1,08 

H 

1,035 

6 

1,00 

8i 

1,085 

4 

1,04 

6^ 

1,065 

9 

1,09 

4i 

1,045 

7 

1,07 

9i 

1,095 

5 

1,05 

7-i 

1,075 

10 

1,1 

Table   showing   the  amount   of  £l  for  any. number  of  years 
under  31,  at  5  and  6  per  cent,  per  annum. 


YEARS. 

5       RATES.        6 

YEARS. 

5        RATES.        6 

1 

1,05000 

1,06000 

16 

2,18287 

2,54035 

2 

1,10250 

1,12360 

17 

2,29201 

2,69277 

3 

1,15762 

1,19101 

18 

2,40662 

2,85434 

4 

1,21550 

1,26247 

19 

2,52695 

3,02560 

5 

1,27628 

1,33822 

20 

2,65329 

3,20713 

6 

1,34009 

1,41852 

21 

2,78596 

3,39956 

7 

1,40710 

1,50363 

22 

2,92526 

3,60353 

8 

1,47745 

1,59385 

23 

3,07152 

3,81975 

9 

1,55132 

1,68948 

24 

3,22510 

4,04893 

10 

1,62889 

1,79084 

25 

3,38635 

4,29187 

11 

1-71034 

1,89829 

26 

12 

1,79585 

2,01219 

27 

3,73345 

4,82234 

13 

1,885Q5 

2,13292 

28 

3,92013 

5,1  n  68 

14 

1,97993 

2,26090 

29 

4,11613 

5,41838 

15 

2,07892 

2,39655 

30 

4,32194 

5,74349 

156 


COMPOUND   INTERS8T. 


Note.  The  preceding  table  is  thus  made—As  100  :  106  :  :  1  : 
1,05,  for  the  first  year;  then,  As  100  :  105  :  :  1,05  ;  1,1026,  »^ 
cond  year,  &c. 

I.  When  P  T  R  are  given  to  find  A. 
Rule.    pXrt=A. 

EXAMPLES. 

1.  What  will  £225  amount  to  in  3  years'  time,  at  5  per  cent 
per  annum  ?  r  • 

Ans.  1,05X1,05X1,05=1,157625,  then  1,157625X225= 

£260  :  9  :  3  3  qrs. 

2.  What  will  £200  atoount  to  in  4  years,  at  6  per  cent,  per 
«»"""» ?  Ans.  £243  2,026s 

3.  What  will  £450  amount  to  in  5  years,  at  4  per  cent,  per 
^n^"°i  ?  Ans.  £547  :  9  :  10  2,0538368  qrs. 

4.  What  will  £500  amount  to  in  4  years,  at  5^  per  cent,  per 
^"^^"^  •  Ans.  £619:8:2  3,8323  qref 

n.  When  A  R  T  are  given  to  find  P. 

a 
Rule. =P 


rt 


EXAMPLES. 


6.  What  principal,  being  put  to  interest,  will  amount  to  £260  : 
9  :  3  3  qrs.  in  3  years,  at  6  per  cent,  per  annum  ? 

260,465626 

1,05X1,05X1,05=1,157625 =£225. 

1,157625 
6.  What  principal,  being  put  to  interest,  will  amount  to  £243 
2,025s.  in  4  j^ears,  at  5  per  cent,  per  annnm  ?  Ans.  £200. 

'7.  What  principa-  will  amount  to  £547  :  9  :  10  2,0538368  qrs. 
in  5  years,  at  4  per  cent,  per  annum  ?  Ans.  £450? 

8  What  principal  will  amount  to  £619  :  8  :  2  3,8323  qrs.  in  4 
years,  at  5^  per  cent,  per  annum  ?  Ans.  £50Q. 

.    TT  ix^Jlx  A  XX  A  aiu  giVuu  lo  una  xi. 

a  which   being  extracted  by  the  rule  of  extrac- 

RuLE.— =rt  tion,  (the  time  given  to  the  question  showing 

p  the  power)  will  give  R. 


COMPOUND   IlfTBSfiST. 


157 


EXAMPLES. 

9.  At  what  rate  per  cent,  will  £226  amount  to  £2G0  :  9  :  3  3 
qrs.  in  3  years  ?  ^W5.  5  per  cent. ' 

260,465625 

'- ^=1,167625,  the  cube  root  of  which 

225 


(it  being  the  3d  power) =1,05=5  per  cent. 


10.  At  what  rate  per  cent,  will  £200  amount  to  £243  •  2  026' 

'^VT^.     .  ^n..  5  pe;  cent.    * 

11.  At  what  rate  per  cent,  will  £450  amount  to  £547  •  9  •  10 
2,0538368  qrs.  in  5  years  ?  Ans.  4  per  cent. 

1^.  At  what  rate  per  cent,  will  £500  amount  to  £619  :  8  •  2 
3,8323  qrs.  in  4  years  ?  Ans.  5j  per  cent* 

IV.  When  P  A  R  are  given  to  find  T. 

a  which  being  continually  divided  by  R  till  no- 

KuLE.--=rt     thing  remains,  the  number  of  those  divisions 
p  will  be  equal  to  T. 

EXAMPLES. 

13.  In  what  time  will  £225  amount  to  £260 :  9  :  3  3  ars  at 
6  per  cent.  ?  ^ 

260,465625                     1,157625                1,1025  1,05 

• =  1,157625 =  1,1025 =1,05— 

_i   *f         .       .  ^'^^  1.05  1,05 

-1,  the  number  of  divisions  being  three  times  sought. 

14    In  what  time  will  £200  amount  to  £243  2,025s.  at  5  ner 

""Vt      wr  -u.  Ans.  4  ye  J 

10.  in  what  time  will  £450  amount  to  £547  :  9  :  10  2  0538368 

qrs  at  4  per  cent.  ?  ^n..  5  years, 

lb.  In  what  time  will  £500  amount  to  £619  :  8  :  2  3  8323 

qrs.  at  5^  per  cent.  ?  ,  .^.4  y^^^^ 

ANNUITIES,  OR  PENSIONS,  IN  ARREARS. 

J^OTE.    U  represents  the   annuity,  pension,  or  yearly  rent: 
A  U  i  a£  before.  ^      ^  > 


158 


COMPOUND    INTEREST. 


A  Table  showing  the  amount  of  £1  annually,  for  any  number 
of  years  under  31,  at  5  and  6  per  cent,  per  annum. 


YEARS. 

5    RATES.     6 

YEARS. 

5    RATE3.     6 

1 

1,00000 

1,00000 

16 

23,65749 

35,67252 

2 

2,05000 

2,06000 

17 

25,84036 

28,21288 

3 

3,15250 

3,18360 

18 

28,18238 

30,90565 

4 

4,31012 

4,37461 

19 

30,53900 

33,75999 

5 

5,52563 

5,63709 

20 

33,06595 

36,78559 

6 

6,80191 

6,97532 

21 

35,71925 

39,99272 

7 

8,14200 

8,39383 

22 

33,50521 

43,33229 

8 

9,54910 

9,89746 

23 

41,43047 

46,99582 

9 

11,02656 

11,49131 

24 

44,50199 

50,81557 

10 

12,57789 

13,18079 

25 

47,72709 

54,86451 

11 

14,20678 

14,97164 

26 

51,11345 

59,15638 

12 

15,91712 

16,86994 

27 

54,66912 

63,70576 

13 

17,71298 

18,88213 

28 

58,40258 

68,52811 

14 

19,59868 

21,01506 

29 

62,32271 

73,63979 

15 

21,57856 

23,27597 

30 

66,43884 

79,05818 

Note.  The  above  table  is  made  thus :— take  the  first  year's 
amount,  which  is  £1,  multiply  it  by  1,05  +  1  =2,05  =  second 
year's  amount,  which  also  multiply  by  l,05+l  =  2,1525=third 
year's  amount. 

T.  When  U  T  R  are  given  to  find  A. 


ur" — u 


RULE.- 


-=A,  or  by  the  table  thus : 


Multiply  the  amount  of  £1  for  the  number  of  years,  and  at  the 
rate  per  cent,  given  in  the  question,  by  the  annuity,  pension, 
&c.  and  it  will  give  the  answer. 

EXAMPLES. 

1*7.  What  will  an  annuity  of  £50  per  annum,  payable  yearly, 
amount  to  in  4  years,  at  5  per  cent.  ? 

Ans.  1,05  X  1,05  X  1,05  X  1,05  X  50=60,77531250 
60,7753125—50 

Ijien =£215  :  10  :  1  2  qrs.;  or, 

1,05—1 
t>y  the  table  thus,  4,31012X50=£215  :  10  :  1  1,76  qrs. 

18.  What  will  a  pension  of  £45  per  annum,  payable  yearly, 
unount  to  in  5  years,  at  5  per  cent.  ? 

Ans.  £248  :  13  :  0  3,27  qis. 


•  COMPOUND   INTEREST. 


150 


19.  If  a  salary  of  £40  per  annum,  to  bo  paid  yearly,  be  for- 
borne 6  years,  at  6  per  cent.,  what  is  the  amount? 

Ans.  £279  :  0  :  3,05796008d. 

20.  If  an  annuity  of  £15  per  annum,  payable  yearly,  be  omit- 
ted to  be  paid  for  10  years,  at  6  per  cent.,  what  is  the  amount? 

Ans.  £988  :  11  :  2,222d. 
II.  When  A  R  T  are  given  to  find  U. 

ar — a 
Rule. =U. 

rt— 1 

EXAMPLES. 

21.  What  annuity,  being  forborne  4  years,  will   amount  to 
^£215  :  10  :  1  2  qrs.  at  5  per  cent.  ?     • 


215,50625X1,05—215,50625 

Ans.  : — =^£50.       . 

1,05X1,05X1,05X1,05—1 

22.  Wliat  pension,  being  forborne  5  years,  will   amount  to 
.£248  :  13  :  0  3,27  qrs.  at  5  per  cent.  ?  Ans.  45. 

23.  What  salary,  being  omitted  to  be  paid  6  years,  will  amount 
to  £279  :  0  :  3,05796096d.  at  6  per  cent.?  Ans.  £40. 

24.  If  the  payment  of  an  annuity,  being  forborne  10  years, 
amount  to  £988  :  11  :  2,22d.  at  6  per  cent.,  what  is  the  annuity? 

Ans  £i*l^ 
ni.  When  U  A  R  are  given  to  find  T. 

ar-j-u — a  which  being  continually  divided  by  R  till 

Rule. =rt     nothing   remains,  the   number  of  those 

u  ,       divisions  will  be  equal  to  T. 

EXAMPLES. 

25.  In  what  time  will  £50  per  annum  amount  to  £216  :  10  : 
1  2  qrs.  at  5  per  cent,  for  non-payment  ? 

Ans.  215,50625X1,05+50 215,50625=1,21550625. 

50 
which  being  continually  divided  by  R,  the  number  of  the  divi- 

01/\Wlo     ^ir»  I  I      1-V/-V  .1.1    ■  A      ■«▼/>#>«<>• 

ojivixp    TYiix    uxi  —  -x    ycaio. 

26.  In  what  time  will  £45  per  annum  amount  to  £248  :  13 
327  qrs.  allowing  5  per  cent,  for  forbearance  of  payment  ? 

Ans.  5  years, 
02  ^ 


160 


COMPOUND    irtTBRBST. 


37.  In  what  time  will  £40  per  annum  amount  to  £279  :  0  : 
3,05796096(1.  at  6  per  cent.  ?  ^ns.  6  years. 

28.  In  what  time  will  £75  per  annum  amount  to  £988  :  11  : 
2,22d.  allowing  6  i)er  cent,  lor  forbearance  of  payment  ? 

Ans.  10  years.    . 


PRESENT  WORTH  OF  ANNUITIES,  PENSIONS,  &,c. 

A  Table  showing  the  present  worth  of  £l  annuity/,  for  any  num- 
ber of  years  under  31,  rebate  at  5  and  6  per  cent. 


YEARS. 

5   RATES,   0 

YEARS. 

5   RATES.   0 

1 

0,93238 

0,94339 

10 

10,83777 

10,10589 

2 

1,85941 

1,83339 

17 

11,^^7400 

10,47726 

3 

2,72324 

2,07301 

18 

11,08958 

10,82700 

4 

3,54595 

3,40510 

19 

12,03532 

11,15811 

5 

4,32947 

4,21230 

20 

12,40221 

11,40992 

6 

5,07309 

4,91732 

21 

12,82115 

11,70407 

7 

5,78037 

5,58238 

22 

13,10300 

12,04158 

8 

0,40321 

0,20979 

23 

13,48857 

12,30338 

9 

,  7,10782 

0,80109 

24 

13,79804 

12,55030 

10 

7,72173 

7,30008 

25 

14,09394 

12,78330 

11 

8,30041 

7,88087 

26 

14,37518 

13,00317 

12 

8,80325 

8,33384 

27 

14,04303 

13,210.53 

13 

9,39357 

8,85908 

28 

14,89812 

13,40010 

14 

9,89804 

9,29498 

29 

15,14107 

13, .59072 

15 

10,37965 

9,71225 

30 

15,37245 

13,70483 

Note.  The  above  table  is  thus  made : — divide  £1  by  1,05=5 
,95238,  the  present  worth  of  the  first  year,  which  — 1,05=90753, 
addexi  to  the  first  year's  present  worth=  1,85941,  the  second 
year's  present  worth  ;  then,  90703—1,05,  and  the  quotient  added 
to  185941  =  2,72327,  third  year's  present  worth. 

I.  When  U  T  R  are  given  to  find  P. 


u 


u- 


RULE.- 


:P. 


r— 1 


Multiply  the  present  worth  of  £1  annuity  for  the  time  and  rate 
per  cent,  given  by  the  annuity,  pension,  &c.,  it  will  give  the  m- 


BWQr. 


COMPOUND    INTUBBBT. 


161 


79  :  0  : 

r^eavft. 

8  :  11  : 


^ears.'    J 

c. 

ly  num- 


589 
726 
7G0 
811 
992 
407 
ir)8 
1338 
i03G 
1336 
1317 
053 
(GIC) 
1072 
i4S3 

1,05  = 
=  90753, 
I  second 
it  added 


and  rate 
!  the  m- 


EXAMPLES. 

29.    What  is  the  present  worth  of  an  annuity  of  £30  per  an- 
num, to  continue  7  years,  at  6  per  cent.  ? 

Ans.  £167  :  9  :  5  ,184d. 


80 


-=19,9517 


1,60363 
=  167,4716. 


30—19,9517  =  10,0483 


10,0483 


By  the  table  5,58238X30=167,4714. 


Ii06— 1 


30.  What  is  the  present  worth  of  a  pension  of  £40  per  annum 
to  continue  8  years,  at  5  per  cent.  ?  ' 

.  Ans.  £258  :  10  :  0  3,264  qrs. 

31.  What  IS  the  present  worth  of  a  salary  of  35,  to  continue 
I  7  years  at  6  per  cent.  ?  Ans.  £195  :  7  :  7  3,968  qra. 

j     32.   What  IS  the  yearly  rent  of  £50,  to  continue  5  years,  worth 
m  ready  money,  at  5  per  cent.  ?        Ans.  £216  :  9  :  5  2,56  qrs. 

ir.  When  P  T  R  are  given  to  find  U. 

prtXr— pr* 
Rule.— — = U. 


r^— 1 


EXAMPLES. 


33.  If  an  annuity  be  purchased  for  £l67  :  9  :  5  184d.  to  b« 
}ntinued  7  years,  at  6  per  cent,  what  is  the  annuity? 

^^*'  107,4716X1,50363X1,06—167,4716X1,50363 


1,50363—1 


=£30. 


34.  If  the  present  payment  of  £258  :  10  :  6  3,264  qrs.  be 
nade  for  a  salary  of  8  yeai-s  to  come,  at  5  per  cent.,  what  is  the 
'^^^•■y-  Ans  £40 

35  If  the  present  payment  of  £195  :  7  :  7  3,968  qrs.  be  're- 
luired  tor  a  pension  for  7  years  to  come,  at  6  per  cent.,  what  is 

Po^ip    ?  ^\^  P^^^^"*  ^^^'^^  ^^  ^^  annuity  5  years  to  come, 'be 
t^iO  :  9  :  6  2,56  qrs.  at  5  per  cent.,  what  is  the  annuity  ? 

Ans.  £50. 
03 


162 


COMPOUND    INTEREST. 


in.  When  U  P  R  are  given  to  find  T. 

u  which  being  continually  divided  by  R  till 

fjuLE. =r*     nothing  remains,  the  number  of  those  di- 

p-f-u — ^pr  visions  will  bo  equal  to  T. 

EXAMPLES. 

37.   How  long  may  a  lease  of  £30  yearly  rent  be  had  for 
£167  :  9  :  5  ,184d.  allowing  6  per  cent,  to  the  purchaser? 

which  being  continually 
1  f^ncjf  Q  divided,  the  number  of 

l,DUdt)d  those  divisions  will  be= 

167,4716+30-177,5198  ^  ^^^  ^^^^^^ 


30 


38.  If  £258  :  10  :  6  3,264  qrs.  i^  ^.aid  down  for  a  lease  of  £40 
per  annum,  at  5  per  cent,  how  long  is  the  lease  purchased  for  ? 

Ans.  8  years. 

39.  If  a  house  is  l6t  upon  lease  for  £35  per  annum,  and  the 
lessee  makes  present  payment  of  £195  :  7  :  8,  he  being  allowed 
6  per  cent.,  I  demand  how  long  the  lease  is  purchased  for? 

Ans.  7  years. 

40.  For  what  time  is  a  lease  of  £50  per  annum,  purchased 
when  present  payment  is  made  of  £216  :  9  :  5  2,56  qrs.  at  5  per 
cent.  ?  ■  ■^^«-  ^  y^^^"^^- 

ANNUITIES,  LEASES,  &c.  TAKEN  IN  REVERSION. 

To  find  the  present  worth  of  annuities^  leases,  <&c.  taken  in 

reversion.  ^ 

Rule.    Find  the  present  worth  of  the  annni-  u 

ty,  &c.  at  the  given  rate  and  for  the  time  of  its     u • 

continuance :  thus,  ^ 


-=?. 


r— 1 


2.  Change  P  into  A,  and  find  what  principal 
being  put  to  inteiest  will  amount  to  V  at  the 
same  rate,  and  for  the  time  to  come  before  the 
annuity  commences,  which  will  be  the  present 
worth  of  the  annuity,  <fec. :  thus 


a 


=P. 


COMPOUND    INTEREST. 


163 


EXAMPLES. 

41.  What  is  the  present  worth  of  a  reversion  of  a  lease  of  £40 
per  annum,  to  continue  for  six  years,  but  not  to  commence  till 
the  end  of  2  years,  allowing  6  per  cent,  to  the  purchaser  ? 

A71S.  £175  :  1  :  1  2  ,048  qrs. 
40                            40—28,1984                            196,6933 
=28,1984 =196,6933       


1,1236 


1,41852  1,06—1 

=  175,0563. 

42.  What  is  the  present  worth  of  a  reversion  of  a  lease  of  £60 
per  annum,  to  continue  1  years,  but  not  to  commence  till  the  end 
ot  3  years,  allowing  5  per  cent,  to  the  purchaser  ? 

.o    rri         .        .  .  ^'^^'  ^299  :  18  :  2,8d. 

43.  Ihere  is  a  lease  of  a  house  at  £30  per  annum,  which  is 
yet  m  being  for  4  years,  and  the  lessee  is  desirous  to  take  a  lease 
ni  revei-sion  for  1  yeai-s,  to  begin  when  the  old  lease  shall  be  ex- 
pu-ed,  what  will  be  the  present  worth  of  the  said  lease  in  rever- 
sion, allowing  5  per  cent,  to  the  purchaser  ? 

Ans.  £142  :  16  ;  3  2,688  qrs. 
* 
To  find  the  yearly/  income  of  an  annuity,  <ftc.  taken  in  reversion. 

Rule.  Find  the  amount  of  the  present 
worth  at  the  given  rate,  and  for  the  time  be- 
fore the  annuity  commences :  thus, 

Change  A  into  P,  and  find  what  yearly  rent 

being  sold  will  produce  P  at  the  same  rate,     

and  for  the  time  of  its  continuance,  which  will    pr^Xr— prt 
be  the  yearly  sura  required :  thus,  l-JJ 


pri=A. 


r*— 1. 


EXAMPLES. 


44.  What  annuity  to  bo  entered  upon  2  years  hence,  and  then 
to  continue  6  years,  may  be  purchased  for  £175  :  1  :  1  2  048  ars 
at  6  per  cent.  ?  .  '        ^  • 


Ans.  175,0563  X  1,1236=196,6933 
hen  196,6933X  1,41852X  J,06— 279,01337 


1,41852—1 


-=£40. 


/ 


164 


COMPOUKD   INTEBBST. 


45.  The  present  worth  of  a  lease  of  a  house  is  £299  :  18  :  2  8d. 
taken  in  reversion  for  7  years,  but  not  to  commence  till  the  end 
of  3  years,  allowing  5  per  cent,  to  the  purciaj^er,  what  is  the 
yearly  rent?  Ans.  60. 

46.  There  is  a  lease  of  a  house  in  being  for  4  years,  and  tho 
lessee  being  minded  to  take  a  lease  in  reversion  tor  7  years,  to 
begin  when  the  old  lease  shall  be  expired,  paid  down  £142  :  16  : 
3  2,688  qi*s.  what  was  the  yearly  rent  of  the  house,  when  the  les-^ 
see  was  allowed  5  per  cent,  for  present  payment  ?        Ans.  £30. 

PURCHASING    FREEHOLD    OR   REAL   ESTATE,    IN    SUCH   AS    ARE 
BOUGHT   TO    CONTINUE    FOR   EVER. 

I.  When  U  R  are  given  to  find  *W. 

u 

Rule. =W. 

r— 1 

EXAMPLES.   • 

-47.  "What  is  the  worth  of  a  freehold  estate  of  £50  per  annum, 
allowing  5  per  cent,  to  the  buyer  ? 

60 

Ans. =£1000. 

1,05—1 

48,  What  is  an  estate  of  £140  per  annum,  to  continue  for  ever, 
worth  in  present  money,  allowing  4  per  cent,  to  the  buyer  ? 

Ans.  £3500. 

49.  If  a  freehold  estate  of  £75  yearly  rent  was  to  be  sold,  what 
is  the  worth,  allowing  the  buyer  6  per  cent.  ? 

Ans.  £1250. 

II.  When  W  R  are  given  to  find  U. 


Rule.  wXr — 1=U. 


EXAMPLES. 


50.  If  a  freehold  estate  is  bought  for  £1000,  and  the  allowance 
of  5  per  cent,  is  made  to  the  buyer,  what  is  the  yearly  rent  ? 

Ans.  1,05— 1  =,05,  then  1000X,05=i260. 

51.  If  an  estate  be  sold  for  £3500,  and  4  per  cent,  allowed  to 


the  buyer,  what  is  the  yearly  rent  ? 


Ans,  £140. 


I 


COMPOUND   INTEREST. 


165 


62.  If  a  freehold  estate  is  bought  for  £1250  present  money, 
and  an  allowance  of  6  per  cent,  made  to  the  buyer  for  the  same! 
what  is  the  yearly  rent  ?  Ans.  £75. 

III.  When  W  U  are  given  to  find  R. 
w-j-u 

KULE.^ =R. 


w 


EXAMPLES. 


53.  If  an  estate  of  £50  per  annum  be  bought  for  £1000,  what 
Is  the  rate  per  cent.  ? 

lOOO-f-50 

Ans. =1,05=5  per  cent. 

1000 

54.  If  a  freehold  estate  of  £140  per  annum  be  bought  for 
£3500,  what  is  the  rate  per  cent,  allowed  ?         Ans.  4  per  cent. 

55.  If  an  estate  of  £75  per  annum  is  sold  for  ^21250,  whatia 
the  rate  per  cent,  allowed  ?  Ans.  6  per  cent. 

PURCHASING    FREEHOLD    ESTATES    IN    REVERSION. 

To  find  the  worth  of  a  Freehold  Estate  in  reversion : 

u 

Rule.  Find  the  worth  of  the  yearly  rent,  thus —      =W 

Change  W  into  A,  and  find  what  principal,  being  r — 1 
put  to  interest,  will  amount  to  A  at  the  same  rate,  and 
for  the  time  to  come,  before  the  estate  commences,  and 
that  will  be  the  worth  of  the  estate  in  reversion,  thus : 


a 


_=P 
r*. 
EXAMPLES. 

66.  If  a  freehold  estate  of  £50  per  annum,  to  commence  4 
years  hence,  is  to  be  sold,  what  is  it  worth,  allowing  the  purchaser 
5  per  cent,  for  the  present  payment  ? 

50  1000 

Ans. =1000,  then =JE822  :  14  :  1^. 

1,05—1  1,2155 

67.  What  is  an  estate  of  £200,  to  continue  tor  ever,  but  not  to 
commence  till  the  end  of  2  years,  worth  in  ready  money,  allowing 
the  purchaser  4  per  cent.  ?  Ans.  £4622  :  15  :  7  ,44d. 

5S.  What  is  an  estate  of  it;240  per  annum  worth  in  ready  mo- 
ney, to  continue  for  ever,  but  not  to  commence  till  the  end  of  3 
years,  allowance  being  made  at  6  per  cent.  ? 

Ans.  £3358  :  9  :  10  2,24  qrs. 


166 


REBATE    OR   DISCOUNT. 


To  find  the  Yearly  Rent  of  an  Estate  taken  in  reversion. 

Rule.   Find  the  amount  of  the  worth  of  the 
estate,  at  the  given  rate,  and  time  before  it  com-     wr*=A 
mences,  thus : 

Change  A  into  W,  and  find  what  yearly  rent     wr — w=U, 
being  sold  will  produce  U  at  the  same  rate,  thus : 
which  will  be  the  yearly  rent  required. 

EXAMPLES. 
69.  If  a  freehold  estate,  to  commence  4  years  hence,  is  sold 
for  $822  :  14  :  1^,  allowing  the  purchaser  5  per  cent.,  what  is 
the  yearly  income  ?  Ans.  822,70025  X  1,2155  =  1000, 

then  1000X1,05— 1000=£50. 

60.  A  freehold  estate  is  bought  for  £4622  :  15  :  7  ,44d,  which 
does  not  commence  till  the  end  of  *2  years,  the  buyer  being  allow- 
ed 4  per  cent,  for  his  money.  I  desire  to  know  the  yearly  in- 
come. Ans.  £200. 

61.  There  is  a  freehold  estate  sold  for  £3358  :  9  :  10  2,24  qrs., 
but  not  to  commence  till  the  expiration  of  3  years,  allowing  G 
per  cent,  for  present  payment ;  what  is  the  yearly  income  ? 

Ans.  240. 
REBATE  OR  DISCOUNT. 

A  Table  shoynng  the  present  worth  of  £l  diie  any  number  of 
years  hence,  under  31,  rebate  at  5  and  6  per  cent. 


YEARS. 

5   RATES.   6 

YEARS. 

5   RATES.   6 

1 

,952381 

,943396 

16 

,458111 

,393646 

2 

,907030 

,889996 

17 

,436296 

,371364 

3 

,863838 

,839619 

18 

,415520 

,350343 

4 

,822702 

,792093 

19 

,395734 

,330513 

5 

,783526 

,747258 

20 

,376889 

,311804 

6 

,746215 

,704960 

21 

,358942 

,294155 

7 

,710682 

,665057 

22 

,341849 

,277505 

8 

,676839 

,627412 

23 

,325571 

,261797 

9 

,614609 

,591898 

24 

,340068 

,246978 

10 

,613913 

,558394 

25 

,295302 

,232998 

11 

,584679 

,526787 

26 

,281240 

,219810 

12 

,556837 

,496969 

27 

,267848 

,207368 

13 

,530321 

,468839 

28 

,255093 

,196630 

14 

,505068 

,442301 

29 

,242946 

,184556 

15 

,481017 

,417265 

30 

,231377 

,174110 

Note. — The  above  table  is  thus 
first  year's  present  worth  ;  and  ,95 
yrar;  and  ,90703-i-l,05=,8(33838 


made  :  1  -^  1,05  =  ,952381, 
2381-M,05=,90703,  second 
third  year,  &c. 


REBATE    OR   DISCOUNT. 

I.  When  S  T  R  are  given  to  find  P. 


167 


Rule. — =P. 


EXAMPLES. 


1.  What  is  the  present  worth  of  £315  :  12  :  4  ,2d,  payable  4 
vears  hence,  at  6  per  cent.  ? 

Ans.  1,06X1,06X1,00X1,06=1,20247,  then  by  the  table. 
315,6175  316,6176 

•=£250  ,792093 


1,26247 


249,9984124275 

2.  If  £344  :  14  :  9  1,92  qrs.  be  payable  in  7  years'  time,  what 
IS  the  present  worth,  rebate  being  made  at  5  per  cent.  ? 

./4w9  £^d-^ 

3.  There  is  a  debt  of  £441  :  17  :  3  1,92  qrs.,  which  is  payable 
4  years  hence,  but  it  is  agreed  to  be  paid  in  present  money ;  what 
sum  must  the  creditor  receive,  rebate  being  made  at  6  per  cent.  ? 

II.  When  P  T  R  are  given  to  find  S.  *  * 

Rule.  pXi'*=S. 

EXAMPLES. 

4.  If  a  sum  of  money,  due  4  years  hence,  produce  £250  for 
t he  present  payment,  rebate  being  made  at  6  per  cent.,  what  was 
the  sum  due  ? 

Jw5.'£250xl,20247=£3l5  :  12  :  42d. 

5.  If  £245  be  received  for  a  debt  payable  7  years  hence,  and 
I  an  allowance  ot  5  per  cent,  to  the  debtor  for  present  payment 

what  was  the  debt  ?  Am.  £344  :  14  :  9  1,92  qrs.    ' 

6.  There  is  a  sum  of  money  duo  at  the  expiration  of  4  years 
but  the  creditor  agrees  to  take  £350  for  present  payment,  allow- 
ing 6  per  cent.,  what  was  the  debt  ? 

Ans.  £441  :  17  :  3  1,92  qrs. 

III.  When  S  P  R  are  given  to  find  T; 

s  which  being  continually  divided  by  R  till  nothing 

Rule.— =rt  remains,  the  number  of  those  divisions  will  be 
p  equal  to  T. 


108 


BEBATS    OR   DISCOUNT. 


EXAMPLES. 

7.  The  present  payment  of  £250  is  made  for  a  debt  of  £316  ; 
12:4  ,2d.,  rebate  at  6  per  cent.,  in  what  time  was  the  debt  pay- 
able? 

315,6175  which  being  continually  divided,  those 

Ans. — =1,26247     divisions  will  be  equal  to  4=the  num- 

250  ber  of  years. 

8.  A  person  receives  £245  now,  for  a  debt  of  £344  :  14  :  9 
1,92  qrs.,  rebate  being  made  at  5  per  cent.  I  demand  in  what 
time  the  debt  was  payable  ?  Ans.  7  years. 

9.  There  is  a  debt  of  £441  :  17  :  3  1,92  qrs.  due  at  a  certain 
time  to  come,  but  6  per  cent,  being  allowed  to  the  debtor  for  tho 
present  payment  of  £350,  I  desire  to  know  in  what  time  the  sum 
should  have  been  paid  without  any  rebate  ? 

Ans.  4  years. 
IV.  When  S  P  T  are  given  to  find  R. 

s  which  being  extracted  by  the  rules  of  extraction, 

Rule. — =r*     (the  time  given  in  the  question  showing  the  pow- 
p  er,)  will  be  equal  to  R. 


EXAMPLES. 

10.  A  debt  of  £315  :  12  :  4,2d.  is  due  4  years  hence,  but  it  is 
agreed  to  take  £250  now,  what  is  the  rate  per  cent,  that  the  re- 
bate is  made  at  ? 

315,6175  4 

Ans.  =  1,26247  :  ^1,26247=1,06=6  per  cent. 

250 

11.  The  present  worth  of  £344  :  14  :  9  1,92  qrs.,  payable  1 
years  hence,  is  £245,  at  what  rate  per  cent,  is  the  rebate  made  ? 

Ans.  5  per  cent. 

12.  There  is  a  debt  of  £441  :  17  :  3  1,92  qrs.,  ppj^ible  in  4 
years  time,  but  it  is  agreed  to  take  £350  present  payruont.  I  de- 
sire to  know  at  what  rate  dcv  cent,  the  rebate  is  mi »:    at? 

A'fiS^  ^  D€!F  C0nt= 


169 


TJiE 


TUTOR'S    ASSISTANT. 


PART  IV. 


DUODECIMALS; 

OR,   WHAT  IS   GENERALLY   CALLED 

Cross  Multvplicaiim,  and  Squaring  of  Dimensions  by  Arti- 
ficers and  Workmen. 

RULE    FOR   MULTIPLYING   DUODECIMALLY. 

tion;  o'?te^fJtiS^^^^^^^  "''"  ""^  corresponding  denomina- 
2.  Multiply  each  term  in  the  multiplicand  (beffinninff  at  th« 

ZoKr    A     '  ?bservmg  to  carry  an  unit  for  every  12,  from 
each  lower  denommation  to  ite  next  superior.  ^      ' 

in  ^tL\*^'?f'r^  "^^T"^  ?^"^^'*P^^  ^^^  multiplicand  by  the  primes 

in  the  multipher,  and  write  the  result  of  each  term  one  nk^ 

more  to  the  nVhf.  hanfl  ^f  fi,...  :^  .y.  _-  1..  ,.      f  ^"^  ^°®  P^*ce 

-_, 5.  .^1  laujc  ill  tHu  muiiiplicand. 

nhet  ^1^  'fi,  ^^  s^me  manner  with  the  seconds  in  the  multi- 
of  tL '  •  !i.*^'  'T\  ^^  '""^  ^'"^  ^^^  P^«ces  to  the  right  hand 
of  those  m  the  multiplicand,  and  so  on  for  thirds,  fourths,  &c 


170 


DUODl^tMALS 


EXAMPLES. 


f.    in.      f.    in. 
1.  Multiply  7  .  9  by  3  .  6. 
Cross  Multiplication     Practice. 

6i  7  .9 


7     9 
3^6 


21.0.0=7X3 
2.3.0=9X3 
3.6.0  =  7X6 
0.4.6=9X6 


23 
3 


27.1.6 


2.  Mulrtply 

3.  Multiply 

4.  Multiply 

5.  Multiply 
'""e.  Multiply 

7.  Multiply 

8.  Multiply 

9.  Multiply 

10.  Multiply 

11.  Multiply 

12.  Multiply 

13.  Multiply 

14.  Multiply 

15.  Multiply 

16.  Multiply 

17.  Multiply 

18.  Multiply 


f.in. 
8.5 
9.8 
8.1 
7.6 
4.7 
7.5.9" 
10.4.5 
75.7 
97.8 
57.9 
75.9 
87.5 
179.3 
259.2 
257.9 
311.4.7 
321.7.3 


3  .  6 


#    Duodecimals. 
7  .9 
2  .  6 


Decimals. 

7,75 
3,5 


3 

10  .  6 


27  .  1.6 


23  .  3—  X3 
3  .  10  .  6X6 

27  .  1.6 


3875 
2325 

27,125 


f.  in 
by  4.  7 
by  7.  6 
by  3.  5 
by  5.  9 
by  3.10 
by  3.  5.3" 
by  7.  8.6 
by  9.  8 
by  8.  9 
by  9.  5 
by  17.  7 
by  35.  8 
by  38.10 
by  48.11 
by  39.11 
by  36.  7.5 
by  9.  3.6 


Facit, 

Facit, 

Facit, 

Facit, 

Facit, 

Facit, 

Facit, 

Facit, 

Facit, 

Facit, 

Facit, 

Facit, 

Facit, 

Facit, 

Facit, 

Facit, 

Facit, 


f. 

in.pts. 

38. 

6.11 

72. 

6 

27. 

7. 

5 

43. 

1. 

6 

17. 

6.10^,,,,, 

25. 

8. 

6.2.3 

79.11. 

0.6.6 

730. 

7. 

8 

854. 

7. 

543. 

9. 

9 

1331.11. 

3 

3117.10. 

4 

6960.10. 

6 

12677. 

6.10 

10288. 

6. 

3 

11402. 

2. 

4.11.11 

2988. 

2.10.4.6 

THE  APPLICATION. 
Artificers'  work  is  computed  by  different  measures,  viz  :— 

1.  Glazing,  and  masons'  flat  work,  by  the  foot. 

2.  Painting,  plastering,  paving,  &c.  by  the  yard. 

3.  Partitioning,  flooring,  roofing,  tiling,  &c.,  by  the  square 
100  feet 


01 


4.  Brick  work,  &c.  by  the  rod  of  16^  feet,  whose  square  is 


272i  feet. 


DUODECWIALS. 


171 


Meamring  hy  the  Foot  Square,  as  Glaziers^  and  MasmV  Flat 

Work. 

EXAMPLES. 


Duodecimals. 
V  .  10  the 
6  .    8  heights 
5  .    4  added. 


feet.    in.    pts. 

233  .  0  .  6  at  14d.  per  ft. 


2d.=i  233 


=   Is. 


19  .  10 

3= windows  in  a  tier. 

59  .    6 

3  .  1 1  in  breadth. 


38  .  10     =  2d. 
0.    0^  =  6  parts. 


178  .    6 
54  .    6  .  o 


210)2711  .  10^ 
i5l3  .  11  .  10^  Ans. 


233  .    0  .  6 

fJ^in^Y  'i  *^^  "^^I^^'  ""^  ^  '^^^^^«  «^  g^^s,  each  measurino'  4 
feet  10  inches  long,  and  2  feet  11  inches  broad,  at  4id  per  foot! 

oi    rpi  •^^*-  ^1  :  18  :  9. 

fi  i'l.        -A  ^""^  ^  win/ows  to  be  glazed,  each  measures  1  foot 

V:f'mSr^^^^^^  '  ''-'  ^^  ^^^^^^'  ^-  --^  -^^  the,  comi 

Ans  oGl  *  ^  *  ^ 
22    What  is  the  price  of  a  marble  slab,' whose  length  is  5  feet 
1  inches,  and  the  breadth  1  foot  10  inches,  at  6s.  per  foot? 

^W5.  £3:1:5. 

Measuring  hy  the  Yard  Square,  as  Paviers,  Painters,  Plas^ 

terers,  and  Joiners. 

Note.  Divide  the  square  feet  by  9,  and  it  will  give  the  num- 
1'  ^^  square  yards. 


ber  of 


P2 


//. 


'^A\ 


172 


DU0DBCIMAL8. 


EXAMPLES. 

23.  A  room  is  to  be  ceil  J,  .vhcst)  length  is  74  feet  9  inches, 
and  width  11  feet  6  incheti;  whai  wlil  it  come  to  at  3s.  lOjd.  per 
yard?  Ans.  £18  :  10  :  1. 

24.  What  will  the  paving  of  a  court-yard  come  to  at  4fd.  per 
yard,  the  length  being  68  feet  6  inches,  and  breadth  54  feet  9 
inches  ? 

Ans.  £1  •  0  :  10. 

25.  A  room  v/as  painted  9*7  feet  8  inches  about,  and  9  feet  10 
inches  high,  whai  does  it  come  to  at  2s.  8^d.  per  yard  ? 

Ans.  £14  :  n  :  1^. 

26.  "What  is  the  content  of  a  piece  of  wainscoting  in  yards 
square,  that  is  8  feet  3  inches  long,  and  6  feet<6  inches  broad, 
and  what  will  it  come  to  at  6s.  7^d.  pei:  yard  ? 

Ans.  Contents,  yards  5.8.7.6 ;  comes  to  ill  :  19  :  6. 

27.  What  will  the  paving  of  a  court-yard  come  to  at  3s.  2d. 
per  yard,  if  the  length  be  27  feet  10  inches,  and  the  breadth  14 
feet  9  inches  ? 

Ans.  £7  :  4  :'5. 

28.  A  person  has  paved  a  court-yard  42  feet  9  inches  in  front, 
and  68  feet  6  inches  in  depth,  and  in  this  he  laid  a  foot- way  the 
depth  of  the  court,  of  5  feet  6  inches  in  breadth ;  the  foot-way  is 
laid  with  Purbeck  stone,  at  3s.  6d.  per  yard,  and  the  rest  with 
pebbles,  at  3s.  per  yard ;  what  will  the  whole  come  to  ? 

Ans.  £49  :  11. 

29.  What  will  the  plastering  of  a  ceiling,  at  lOd.  per  yard, 
come  to,  supposing  the  length  21  feet  8  inches,  and  the  breadth 
14  feet  10  inches?       ' 

Ans.  £1:9:9. 

30.  What  will  the  wainscoting  of  a  room  come  to  at  6s.  per 
square  yard,  supposing  the  height  of  the  room  (taking  in  the  cor- 
nice and  moulding)  is  12  feet  6  inches,  and  the  compass  83  feet  8 
inches,  the  three  window  shutters  each  7  feet  8  inches  by  0  feet 
6  inches,  and  the  door  1  feet  by  3  feet  6  inches  ?  The  shutters 
and  door  being  worked  on  both  sides,  are  reckoned  work  and 


half  work. 


Ans.  £36  :  12  :  2J, 


*Cfc 


DUODECIMALS. 


its 


Measuring  hy  the  Square  of  100  feet,  as  Flooring,  Partition^ 

ing,  Roofing,  Tiling,  dc  • 

EXAMPLES. 

,  ?]\  ^f  ^'^i^^.^  10  inches  in  length,  and  10  feet  7  inches  in 
height  of  partitioning,  how  many  squares  ? 

^4^  ^w*.  18  squares,  39  feet,  8  inches,  10  p. 


32.  If  a  house  of  three  stories,  besides  the  ground  floor,  was  to 
be  floored  at  £b:  10  per  square,  and  the  house  measured  20  to 
8  nches,  by  16  feet  9  „i.hes;  there  are  7  fire-places,  whose  n.7 
sures  are,  two  of  6  feet  by  4  feet  6  inches  each,  two  of  6  feet  by 
0  teet  4  inches  eacli,  and  two  of  5  feet  8  inches  by  4  feet  8  inches 
each,  and  the  seventh  of  5  feet  2  inches  by  4  fe'et,  and  the  wel 
hoe  for  the  staii-s  is  10  fe.t  6  inches  by  8  feet  9  inches:  what 
will  the  whole  come  to  ? 

Ans.  £53  :  13  :  3^. 

33  If  a  house  measures  within  the  walls  52  feet  8  inches  in 
length,  and  30  feet  6  inches  in  breadth,  and  the  roof  be  of  a  true 
pitch,  what  will  It  come  to  roofing  at  10s.  6d.  per  square  ? 

Ans.  £12  :  12  :  llf. 

fl  ^fl""?'    In  tiling  roofing,  and  slating,  it  is  customary  to  reckon 
he  flat  and  ha     of  the  building  within  the  wall,  to  be  the  meagre 
ot  the  1  oof  of  that  building,  when  the  said  roof  is  of  a  true  pitch 
J.  e.  when  the  rafters  are  f  of  the  breadth  of  the  building;  but  if 

ll  'T  /'/r'^^'  ^"'^  ^^^^  ^^''  *^"^  P^^^^'  t^^y  "^easlire  from 
one  side  to  the  other  with  a  rod  or  string: 

34.  What  will  the  tiling  of  a  barn  cost,  at  25s.  6d.  per  square : 
the  length  being  43  feet  10  inches,  and  breadth  27  feet  5  inches 
on  the  flat,  the  eave  boards  projecting  16  inches  on  each  side  ? 

Ans.  £24  :  9  :  5i 

Measuring  hy  the  Rod. 

Note  Bricklayer  always  value  their  work  at  the  rate  of  a 
bnck  and  a  half  thick ;  and  if  the  thickness  of  the  wall  is  more  or 
less,  It  must  be  reduced  to  that  thickness  by  this.  // 


174 


DUODECIMALS. 


Rule.  Multiply  the  area  of  the  wall  by  the  number  of  half 
bricks  in  tlie  thickness  of  the  wall;  the  product  divided  by  3, 
gives  the  area. 

EXAMPLES. 

35.  If  the  area  of  a  wall  be  4085  feet,  and  the  thickness  two 
bricks  and  a  half,  how  many  rods  doth  it  contain  ? 

Atis.  25  rods.    ^  ^ 

36.  If  a  garden  wall  be  254  feet  round,  and  12  feet  1  inches 
high,  and  3  bricks  thick  how  many  rods-doth  it  contain? 

Ans.  23  rods,  136  feet  1  in. 

37.  How  many  squared  rods  are  there  in  a  wall  62^  feet  long, 
14  feet  8  inches  high,  and  2^  bricks  thick  ? 

Ans.  5  rods,  166  feet  6  in. 

38.  If  the  side  walls  of  a  house  be  28  feet  10  inches  in  lengtli, 
and  the  height  of  the  roof  from  the  ground  55  feet  8  inches,  and 
the  gable  (or  triangular  part  at  top)  to  rise  42  course  of  bricks, 
reckoning  4  course  to  a  foot.  Now,  20  feet  high  is  2^  bricks 
thick,  20  feet  more  at  two  bricks  thick,  15  feet  8  inches  more  at 
li  brick  thick,  and  the  gable  at  1  brick  thick;. what  will  the 
whole  work  come  to  at  £o  16s.  per  rod? 

Ans.M8:l2:1. 


Multiplying  several  figures  hy  several^  and  the  product  to  he 
produced  in  one  line  only. 

Rule.  Multiply  the  units  of  the  multiplicand  by  the  units  of 
the  multipher,  setting  down  the  units  of  the  product,  and  carry  the 
tens ;  next  multiply  the  tens  in  the  multiplicand  by  the  units  of 
the  multiplier,  to  which  add  the  product  of  the  units  of  the  multi- 
pHcand  multiplied  by  the  tens  in  the  multiplier,  and  the  tens  car- 
lied  ;  then  multiply  the  hundreds  in  the  multiplicand  by  the  units 
of  the  multiplier,  adding  the  product  of  the  tens  in  the  multiplicand 

lY»ilHir\lin/l    \\\7  fV»£i    f^no    \r\    +Vip    rvmlf irilini*     nr»/-l    ^\\r\   iiy>ifct    ^^    fl».-v    %^«i1fi. 

plicand  by  the  hundreds  in  the  multipher ;  and  so  proceed  till  you 
the  multiphcand  all  through,  by  every  figure  of 


the  multiplier. 


* 


DUODECIMALS. 


176 


EXAMPLES. 


Multiply 35234 

by #62424 


Common  way. 
35234 
62424 


Product,  1847107216 


140936 
70468 

140936 

70468 
176170 


1847107216 

EXPLANATIONS. 

Firet,  4X4=16    that  is  6  and  carry  one.     Secondly,  3x4+ 

TV  ll''oli  ^^f  ''  '""^^^'  ^^  ^^-''^  ^1«^"  1  and  carry  I 
Ihirdly  2X4+3X2  +  4x4+2  carried  =  32,  that  is  2  and^cat 
ry  3      Fourthly,  5  X  4+2  X  2  +3  X  4+  4x  2+3  carried  =  47 

'^f7,Vr'^  Z'^  '•     ™'^y^  3  X  4  +  5  X  2  +  2  X  4+3X2 

TsX  4^+rx  2+ s'i'V!?""  'r^  ""^^  ''  SixthbT3X2 
r  Q  Ti  o  +  ^  ^  ^+^  carried  =  51,  set  down  1  and  carrv 
Ll  r"'^^'  r'^i'it  5X2  +  2X5  +  5'carried=37,  that's  7 
and  carry  3      Eighthly,  3X2+5x5+3  carried=34,    et  down 

tinlH  T'V'  ,  ^fi'^'  '  ^  '  +  ^  carried=18,  which  being  mul 
tiphed  by  the  last  figure  in  the  multiplier,  set  the  whole  down 
and  the  work  is  finished.  ' 


176 


THE 


TUTOR'S    ASSISTANT 


PART   V. 


A  COLLECTION  OF  QUESTIONS. 

1.  What  is  the  value  of  14  barrels  of  soap,  at  4^d.  per  lb.,  each 
barrel  containhig  254  lb.  ?  Ans.  £66  :  13  :  6. 

2.  A  and  B  trade  togetlier ;  A  puts  in  £320  for  5  months,  B 
•  £460  for  3  months,  and  they  gained  £100 ;  what  must  each  man 

i-eceive  ?  Ans.  A  £53  :  13  :  9|if ,  and  B  £46  :  6  :  2^\\.    . 

3.  How  many  yards  of  cloth,  at  17s.  6d.  per  yard,  can  I  have 
for  13  cwt.  2  qrs.  of  wool,  at  14d.  per  lb.  ? 

,    -    ^  ,  Ans.  100  yards,  3i  qrs. 

4.  1  I  buy  1000  ells  of  Flemish  linen  for  £90,  at  what  may  I 
sell  It  per  ell  in  London,  to  gain  £10  by  the  whole  ? 

Ans.  3s.  4d.  per  ell. 

5.  A  has  648  yards  of  cloth,  at  14s.  per  yard,  ready  money, 
butm  barter  will  have  16s.;  B  has  wine  at  £42  per  tun,  ready 
money :  the  question  is,  how  much  wine  must  be  given  for  the 
cloth,  and  what  is  the  price  of  a  tun  of  wine  in  barter  ? 

Ans.  £48  the  tun,  and  10  tun,  3  hhds.  12f  gals,  of 
wine  must  be  given  for  the  cloth. 

6.  A  jeweller  sold  jewels  to  the  value  of  £1200,  for  which  he 
received  in  part  876  Fiench  pistoles,  at  16s.  6d.  each;  what  sum 
remains  unpaid  ?  Ans.  k^ll  :  6. 

y.  An  oilman  bought  417  cwt.  1  qr.  15  lb.,  gross  weight,  of 
tram  oil,  tare  20  ^b.  per  112  lb.,  how  many  neat  gallons  were 
there,  allowing  n\  ib.  to  a  gallon.  ?  Ans.  5120  gallons. 

8.  If  I  buy  a  yard  of  cloth  for  14s.  6d.,  and  sell  it  for  16s.  9d., 


uu  i  gam  per  cent. 


Ans. 


9.  ?.ought  27  bags  of  ginger,  each  weighing  ^ , 

.^t  1^  lb   per  bag,  tret  4  lb.  per  104  lb.,  what°do  they 


at  b^d.  per  lb.  ? 

\ 


£15  :  10  :  4yVV 

Gfross  84-^  lb.,  tare 

come  to 


Ans.  £76  :  13  :  1-i^ 


rff* 


A  COLLECTION  OP  QUESTIONS. 


177 

cost?'  ^^  *  ""^  ^"^  ''"''"^  "^'^  ^  ^^  ^  '^""^"°,  what  will  I  of  H  lb. 
11    Ti?s  ^/?        ,1  ^    „  Ans.  17s.  6d. 

11,  If  I  of  a  gallon  cost  f  of  a  pound,  what  will  f  of  a  tun  cost  ? 

19      A     „«„+!  1  ^^*-  -£105. 

1^.  A  gentleman  spends  one  day  with  another,  £]  •  7  •  IQk 
and  at  the  year's  end  layeth  up  ^340,  what  is  his  yearly  income  J 

tirne^'n.ir  If/^'t '^^^'^  ^  ^^"^  ^Cj'e^ch  Iting^l'g. 
times  H2  lb  B  has  39  cii^ks  of  tin,  each  3S8  lb,  how  many  ounces 
difference  is  there  in  the  weight  of  these  commodities  ?       ^     »? 

TA    K        +  •  1    ,  ^*^-  212160  oz. 

14  A  captain  and  160  sailors  took  a  prize  worth  £1360  of 
which  the  captam  had  i  for  his  share,  and  the  rest  was  equally 
chvided  among  the  sailors,  what  was  each  man's  part  ?  ^      ^ 

1  r;    A .  ^r:  ^^^  ^^P^^^""  ^'^^  •^^^^'  ^^^^d  each  sailor  £6:16 
15.  At  What  rate  per  cent,  will  £956  amount  to  £1314  •  10 

'"  16^  r h'  fh   o7^'  ^^''''''' ;  ^^^-  '5  per  cent.    ' 

£13  Aw  \  ''""i'  """.f  ^?'-  ^''^^^^'  ^''^  ^  7  J^^^rses,  worth 
£13  a  piece,  hovv  much  will  make  good  the  difference,  n  case 
they  interchange  their  said  drove  of  cattle  ?  Ans  £4  •  lo 

J\  \T-  fT^  ^r''  ^}^^  ^^  ^'  ^^^^^^  *^  three  pers^ons, 
InA  n      '      V      ^  ""  ".^'^'^  unknown ;  B  twice  as  much  as  A 
and  C  as  much  as  A  and  B ;  what  was  the  share  of  each  ? 

IS   £innn-   f    ^    ^--i   /'^^- ^  ^^0,  B  £40,  and  6  £60. 

IS.  £1000  is  to  be  divided  among  three  men,  in  such  a  imn 
ner,  that  if  A  has  £3,  B  shall  hav^  ^5,  and  C  ^8    itw  mub 
rau3t  each  man  have  ?  ' 

ia    A     .         .^''^^^  •^^^'^  •  ^^'  ^  ^312  :  10,  and  C  i^SOO, 
,    19.  A  piece  of  wainscot  is  8  feet  6^  inches  long,  and  2  feet  95 
inches  broad,  what  is  the  superficial  content  ? 

,„  .u  u  .  ?  ^^^  ¥  "'  garrison,  and  have  provisions  for  G 
months,  but  hearing  of  no  relief  at  the  end  of  5  months,  how  many 
men  must  depart  that  the  provisions  may  last  so  much  the  longer'^ 

01    Ti     1        /•  o         ,        .  ^^^^^*  2^S  men. 

21.  The  less  of  2  numbers  is  187,  their  difference  34,  the  square 

no  ^Pf  ^"^t  ^^  ^■'^^""'':^  ^  ^W5.  1707920929.       * 

oxen  at  f  11,  cows  at  40s.,  colts  at  £1  :  5,   and  hoo-s  fit  £l  •  if. 

number,  how 


buy? 


lany  of  each  sort  did  he 


Ans.  13  of  each  sort,  and  ^£8 


^vJ.  What  number  added  to  11|  will  produce  36^ 


over. 


31  3 
I  0 


A7is.2i^\l        J^ 


178 


A    COLLECTION    OF    QUESTIONS. 


24.  What  number  multiplied  by  ^  will  produce  IIW' 

Ans.  26f  f 

25.  What  is  the  value  of  1*79  liogsheads  of  tobacco,  each  weiffh- 


is  the 
:£2: 


_6_8_ 
10  0' 


Ans.  1^. 


ing  13  cwt.  at  £'I:  7  :  I  per  cvvt.  ?  Ans.  £5478  :  2  :  11. 

20.  My  factor  sends  me  word  he  has  bought  goods  to  the  va- 
lue of  £'500  :  13  :  6,  upon  my  account,  what  will  his  commission 
come  to  at  3|  per  cent.  ?  Ans.  £17:10:52  qi-s.    ' " 

27.  If  ^  of  G  bo  three,  what  will  I  of  20  be  ? 

as.  What  is  the  decimal  of  3  qi-s.  14  lb.  of  a  cwt.  ? 

^  Ans.  ,875 

29.  How  many  lb.  of  sugar  at  4|d.  per  lb.  must  be  given  in 
barter  for  60  gross  of  inkle  at  8s.  8d.  per  gross  ? 

Ans.  1386f  lb. 

30.  If  I  buy  yarn  for  9d,  the  lb.  and  sell  it  again  for  13|d.  per 
lb.,  what  is  the  gain  per  cent.  ?  Mns.  £50. 

3?.  A  t^^baci'onist  would  mix  20  lb.  of  tobacco  at  9d.  per  lb. 
with  60  lb.  at  12d.  per  lb.,  40  lb.  at  18d.  per  lb.,  and  with  12  lb. 
at  2s.  pel  !b.,  what  is  a  pound  of  this  mixture  worth  i 

Ans.  Is.  2id.  /y. 

32.  What  .s  the  difference  between  twice  eight  and  twenty, 
and  twice  twenty-eight ;  as  also,  between  twice  five  and  fifty,  and 
twice  fifty-five  ?  ^  Ans.  20  and  50. 

33.  Whereas  a  noble  and  a  mark  just  15  yards  did  buy ;  how 
many  ells  of  the  same  cloth  for  £qO  had  I  ?  Ans.  600  ells. 

34.  A  broker  bough':  for  his  principal,  in  the  year  1720,  ^2400 
capital  stock  in  the  South-Sea,  at  £650  per  cent.,  and  sold  it 
again  when  it  was  worth  but  £130  per  cent.;  how  much  was 
lost  in  the  whole  ?  Ans.  ^£2080. 

35.  C  hath  candles  at  6s.  per  dozen,  ready  money,  but  in  bar- 
ter will  have  6s.  6d.  per  dozen ;  D  hath  cotton  at  9d.  per  lb.  ready 
money.  I  demand  wh;  '.  price  the  cotton  must  be  at  in  barter ; 
also,  how  much  cotton  must  be  bartered  for  100  doz.  of  candles? 

Ans,  The  cotton  at  9cl.  3  qrs.  per  lb.,  and  7  cwt.  0  qrs. 
16  lb.  of  cotton  must  be  giv^-'  for  100  doz.  candles.* 

36.  If  a  clerk's  salary  be  £12  ay.       what  is  that  per  day  ? 

'-Aon  a      Aj» 

37.  B.  hath  an  estate  of  £53  per  annum,  and  payetb  5s.  lOd. 
to  the  subsidy,  what  must  0  pay  whose  estate  ia^vorth  £100  per 
annum?  ^we.  lis.  Od.  yV 


\ 


A   COLLECTION    OF    QUESTIONS. 


179 


38.  If  I  buy  100  yards  of  riband  at  3  yards  for  a  shilling,  and 
100  more  at  2  yards  for  a  shilling,  and  sell  it  at  the  rate  of  5  yards 
for  2  shiUings,  whethgA  I  gain  or  lose,  and  how  much  ? 

^^  Ans.  Lose  3s.  4d. 

39.  What  number  is  that,  from  which  if  you  take  f ,  the  re- 
mainder Avill  be  g-  ?  jifig  3£^ 

40.  A  farmer  is  willing  to  make  a  mixture  of  rye  at  4s.  a  bushel, 
barley  at  3s.,  and  oats  at  2s. ;  how  much  must  he  take  of  each  to' 
sell  it  at  2s.  6d.  the  bushel  ? 

Ans.  6  of  rye,  6  of  barley,  and  24  of  oats. 
,  41.  If  f  of  a  ship  be  worth  £3740,  what  is  the  worth  of  the 
whole  ?  ^1^5.  £9973  ;  6  :  8. 

42.  Bought  a  cask  of  wine  for  £62  :  8,  how  many  gallons  were 
in  the  same,  when  a  gallon  was  valued  at  5s.  4d,  ? 

Ans.  234. 
^  43.  A  m#ry  young  fellow  in  a  shor^  time  got  the  better  of  i  of 
his  fortune ;  by  advice  of  his  friends  he  gave  £2200  for  an  ex- 
empt's place  in  the  guards ;  his  profusion  continued  till  he  had  no 
jnore  then  880  guineas  left,  which  he  found,  by  computation,  was 
5%  P'^vi't  of  his  money  after  the  commission  was  bought ;  pray  what 
Avas  his  fortune  at  first  ?  J ws.  £10,450. 

44.  Four  men  have  a  sum  of  money  to  be  divided  anion o-st 
them  in  such  a  manner,  that  the  first  shall  have  ^  of  it,  the  second 
I,  the  third  ^,  and  the  fourth  the  r^nainder,  which  is  £28,  what 
is  the  sum?  Ans.  £112. 

45.  Wi)at  is  the  amount  of  £1000  for  5|  years,  at  4f  per  cent, 
simple  interest?  Ans.  £1261  :  5. 

46.^  Sold  goods  amounting  to  the  value  of  £700  at  two  4  months, 
what  is  the  present  worth,  at  5  per  cent,  simple  interest  ? 

yi?is.  £082  :  19  :  5i  yVVr- 

47.  A  room  30  feet  long,  and  18  feet  wide,  is  to  be  covered  with 
painted  cloth,  how  many  yards  of  ^  wide  will  cover  it  ? 

Ans.  80  yards, 

48.  Betty  told  her  brother  George,  that  though  her  fortune,  on 
her  marriage,  took  £19,312  out  of  her  ftmiily,  it  was  but  -f  of  two 
ye&m*  rent,  Heaver  be  praised !  of  his  yearly  income ;  pray  what 
was  that?  Ans.'xWfif"^,  :6:8a  year. 

49.  A  gentleman  having  50s.  to  pay  ^imr  his  labourers  for  a 
day's  work,  would  give  to  every  boy  6d.,  to  every  woman  8d., 
and  to  every  man  16d, ;  the  number  i)f  boys,  wonien,  and  men, 
was  the  same.     I  demand  the  number  of  each  ? 

Ans.  20  of  each. 


180 


A    COLLECTION    OF    QUESTIONS. 


[\ 


60.  A  stone  that  measures  4  feet  6  inches  long,  2  feet  9  inches 
broad,  and  3  feet  4  inches  deep,  how  many  solid  feet  doth  it  con- 

*'*";^i*    ^^Tu  .1         .       ,    ,  •^^'-  41  ^^^^  3  inches. 

oi.  What  does  the  whole  pay  of  a  man-of-war's  crew,  of  640 
sailors,  amount  to  for  32  months'  service,  each  man's  pay  being 
22s.  6d.  per  month  ?  Ans.  £23,040. 

52.  A  traveller  would  change  500  French  crowns,  at  4s.  6d. 
per  crown,  into  sterling  money,  but  he  must  pay  a  halfpenny  per 
crown  for  change ;  how  much  must  he  receive  ? 

Ans.  £111  :  9  :  2. 

53.  B  and  C  traded  together,  and  gained  £100 ;  B  put  in  £640 
C  put  m  so  much  that  he  might  receive  £60  of  the  gain.  I  de- 
mand how  much  C  put  in  ?  •  Ans.  £960. 

54.  Of  what  principal  sum  did  £20  interest  arise  in  one  year 
at  the  rate  of  5  per  cent,  per  annum  ?  Ans,  £400.    ' 

55.  In  672  Spanish  guilders  of  2s.  each,  how  many  French  pis- 
toles, at  17s.  6d.  per  piece?  *  Ans.  762.1. 

56.  From  7  chv^cses,  each  weighing  1  cwt.  2  qre.  5  lb.,'' how 
many  allowances  for  seamen  may  be  cut,  each  weighing  5  oz  7 

'^''fi^  V.  •  ^^*-  3563ii 

o7.  If  48  taken  from  120  leaves  72,  and  72  taken  from  91 
loaves  19,  and  7  taken  from  thence  leaves  12,  what  number  is 
that,  out  of  which  when  you  have  taken  48,  72,  19,  and  7,  leaves 
'  Ans.  158 

58.  A  farmer  ignorant  of  nlfmbere,  ordered  £500  to  be  divided 
among  his  five  sons,  thus  :r-Give  A,  says  he,  i,  B  ^,  C  i,  D  i, 
and  E  |  part ;  divide  this  equitably  among  them,  according  to 
their  father's  intention. 

Ans.  A  £l52ff  |.,  B  £ll4iif,  C  £9Uf }, 
I>  £76111  E  £65i|f . 

59  When  first  the  marriage  knot  was  tied 

Between  my  wife  and  me, 
My  age  did  hers  as  far  exceed, 

As  three  times  three  does  three ; 
But  when  ten  years,  and  half  ten  years, 

We  man  and  wife  had  been, 
Her  age  came  then  as  near  to  mine, 
As  eight  is  to  sixteen, 

ues,   ¥v  flat  wa»  eaca  oi  our  ages  when  we  were  married  ? 

Ans.  45  years  the  man,  15  the  woman. 


A   COLtBCTIOy   OP   QUESTIONS. 


181 


SUPPLEMENTAL  QUESTIONS. 

2.  The  less  of  two  numbers  is  17  nnri  oA     i,    •     ^'**- 462s. 

tracted;  what  is  that  number"  "^  *<*  ™'"'  ^"1'- 

4.  Of  three  numbers,  the  fint  is  2Ti  <•  <. .        7  •    ;^'"'-  ^^^• 
third  is  as  much   as  the  otW  1      '  u   '"'°''"'' '' ^1"' ^d  the 
three  numbera!  "  """'   "•>"'   '^  «><=  s"m  of  the 

whL'sufr  5  °'  ''^^  ""'""^■^  '^  ^«  »<•  '"e  diff-n'ie^s' 37 ; 

:^^t^;^,fhra^"^:,--X^^^^^^^^ 

9-   After  having  added  successivelv  11   20    qo      i"!"/^- 

,  .8  b;  SLTo^'ttf^  t;"^  r.'^r/i' ''."» ^-- -^'  'f 

!  "ill  be  equal ;  what  is  the  I^el^e'h  t  "  "'"  ""'''  "'^'^  "S' 

is  the  greater  t  *  "'^'''  ""=  ■'emainder  is  244 ;  what 

Iffreater  ?  ^  "^  *^^  ""^^^"^  ^^'^'^  total  is  145;  what  is  iK- 

Ans.  The  smallest  1,046,  the  mean  1,120. 


■4i 


■mn ' 


^82 


A    COLLECTION   OF   UUESTKTHg. 


h 


•■^^j  ;f/L^''  dividing  a  certain  sum  between  26  persons  each  re. 
ceived  257s. ;  what  was  the  sura  ?  Ans.  6  682s 

16.  From  a  certain  sum  152  persons  took  $17  each*  and  there 
remamed  $13;  what  was  tlie  sura  ?  Jns.  $2597 

17.  What  is  the  niimber  that  being  augn- anted  by  56  mid  'di- 
vided by  55,the  quotient  will  be  2,854  ?  Ans.    156  914 

18.  What  is  the  number  that  being  divided  by  27  gives  a 
quotient  equal  to  the  product  of  1,091  by  3  ?  Ans  88  371 

19  By  selling  120  yards  of  cloth  for  3,600s.  tliere  was  fls 
profit  per  yard  ;  what  was  the  buying  price  ?  Ans.  3,000s. 

20  I  bought  150  yards  of  cloth  for  3,7508.  and  sold  them  for 
oi    Uu '"^ '  "^^'^^  "^'^  ^  S^"'  ^3^  ^he  bargain  ?         Am.  60Qs. 

o^nl'.nu^*,'"^.'^^''^?  ^^  obtained,  if,  after  having  multipUed 
Jo0,540  by  10  this  product  should  be  repeated  2,458  times? 

on    A  1       <m  ^"*-  6,158,273,200. 

22.  A  man  has  $3000  revenue  and  spends  $5  per  day;  what 
will  he  lay  up  at  the  end  of  10  years  ?  Ans.  $11,750. 

23.  A  class  is  composed  of  a  certain  number  of  scholars ;' if 
there  were  8  more  the  number  would  be  augmented  i ;  how  manv 
scholars  were  there  ?  Ans  40  ' 

24.  The  quarter  of  the  54th  part  of  a  number  is  5,454*;  what 
1^  that  number  ?  ^^,  1,178,064. 

25.  On  the  sale  of  150  j^rds  of  cloth  for  29s.  per  yard,  there 
were  600s.  profit ;  what  was  the  buying  price  ?        Ans.  3,750s. 

26.  What  number  being  divided  by  4  gives  a  quotient  such 
that,  atter  subtracting  9,  the  remainder  will  be  20  ?      Ans.  116. 

27.  How  many  revolutions  will  the  second-hand  of  a  clock 
make  in  a  year,  the  year  behig  365d.  5h.  48min.  ? 

oo     A  1      .         ,     ,  ^^*-  525,948  rev. 

^8.  A  number  is  such  that  in  taking  9  from  its  fourth  part,  the 
remainder  is  91  ;  what  is  |^e  number  ?  Ans.  400. 

29.  Wliat  is  the  imf^^ev  whose  17th  part  auffmented  54,'  is 
eijual  to  002  ?  .  -  ^  ^4,^^^  ^  3  jg'^ 

30.  What  number  added  to  the  product  of  186  by  27,  givea 
1 15  times  155  for  total  ?  Ans.  12  830. 

31.  llio  less  of  two  numbers  is  187,  and  their  difference  is  34; 
required  the  square  of  their  product  ?  Ans.  1,707,920,929. 

32.  What  number  must  be  added  to  the  square  of  125'to  pro- 
duce 20,000  for  total  ?  Ans.  4,375. 

30.  The  siihj  of  two  numbers  is  860,  and  the  less  is  144  ;  re- 
quired the  result  of  their  product  by  the  square  of  their  difference? 

Ans.  161,243,136. 


\ 


/    , 


A   COLLECTION   OP  QVBBWOlTS.  1^ 

fT,  ^^Z^^""  """;^!?  ^'^  '"'^'  *^*^  *^«  g'-eater  is  37  times  45  and 
their  difference  19  times  4 ;  required  tht  two  numbere  their  diffL 
ence,  their  sum  and  their  product?  "woers,  meir  difter- 

ins.  The  two  numbers  are  1,665  and  1,589  • 

o^   rri.  .         **'"•  '^5  sum  3,254;  prod  2  64'ifi8»; 

35.  The  suras  of  two  numbers  i<*  4.  *;  i  ^  JAZ     -%'^f  0'«»5. 

38.  There  are  two  numbera,  one  is  39  and  the  aiCTi^o^V' 
greater;  required  their  sum  a^d  the  «ql?e  of  tliXe^^^er'' 

156,970  fofp^duc^"""'"  ^^'-'^^'-S  """^"f'^d  ^  5^-  gi- 

Willi  ma'  •"  '""'"P''^''  "y ''"  »"'^--  n„mbeM^';f,S„,e 

41.  By  what  number  must  54  be  multiplied  to  give  9;990 /' 

1,  "s  !ii-Si::zf  ""'"'^'  '^ ''  ^-  4x " 

43   The  sum  of  two  numbe.,  is  13,  and  their  predict  divfded 

jj   Ti  i»  ,  ^?i*.  9  and  4. 

154    wW '""'/'''' r'"?'''  ^'  2,458,  and  their  difference  i. 
154    what  are  the  iiumbei^  ?    Ans.  1,152  and  1,306. 

4&.  Keqmred  two  numbers  whose  difference  is  7,  and  sum  33  ? 

4fi   Ti,«  ^-a-  1   .  ^"*-  20  and  13. 

40    ihe  ditterence  between  two  nnmbere  is  100,  and  after  takinff 

i"    i  .„  •    ^=  ^'*''  "'1  and  171. 

his  a»A .   T."-   .t''^''"  '^'"'^""  *^*"  ''''  '■»*er  who  is  four  time, 
to  age ;  what  .s  the  age  of  each  ?  Am.  60  and  15. 

tlieir  aiye,  ifo,"'  "  ""  "T.i^."''^  "^  ^^  '»'''  «"<'  tl-o  ™™  "f  both 
«ie,r  ages  ,s  91 ;  required  their  ages »  Ans.  *  and  13. 

the  L'.,^"       ^'  father  and  son  together  is  80  yeara,  and  if 

tue  sons  ajre  was  dnuhlaA   i+ ,^^„ij  u-   i/n  .  •'       .' 

taHiAp'c.  „,if  A  •   '    -—----••--.•-  TTvui;^  uu  iu  jeaiB  more  tiiau  im 

60    F-    if   ''  '^'K''^  ^^'^''  'Ses  ?  Ans.  50  and  30. 

of  the  other  ?       ""  '  ''^^'^  '"""  ^'  ^^®  '  ^"'^  '^'^^  ^^^  ^"^-fi^t^^ 

^m.  90  and  18. 


184 


A    COLLECTION    OF   QUESTIONS. 


ier; 


51.   54  years  is  the  age  of  the  father  and  son  to£ 
father  is  22  years  older  than  the  son ;  what  is  the  age  of  each  ? 

Ans.  38  and  16. 
62.  Two  numbers  are  such  that  by  adding  160  to  the  less,  they 
are  equal,  and  their  sum  is  2,400 ;  what  are  the  numbers  ? 

Ans.  Greater  1,275,  less  1,125. 

53.  The  sum  of  two  numbers  is  2,588  and  to  make  them  equal 
add  178  to  the  less ;  what  are  the  numbers? 

Ans.  1,383  and  1,205. 

54.  The  sum  and  difference  of  two  numbers  are  150  and  100; 
what  is  their  quotient  ?  Ans.  5 

55.  If  I  had  as  many  more  half  dollars  as  I  have,  after  spend- 
ing 18, 1  would  still  have  194 ;  how  many  have  I?     Ans.  106. 

56.  The  sum  of  two  numbers  is  2,587,  to  make  them  equal  sub- 
tract 178  from  the  greater  and  add  17  to  the  less;  what  are  the 
numbers?  Ans.  1,196  and  1,391. 

57.  The  difference  between  two  numbers  is  10,  and  their  quo- 
tient is  three ;  what  are  the  numbers?  Ans.  5  and  15. 

58.  Required  to  divide  60  into  three  parts,  so  that  the  first  may 
be  8  more  than  the  second  and  16  more  than  the  third  ? 

Ans.  28,  20  and  12. 
69.  The  divisor  and  dividend  together  make  180  and  their 
quotient  is  1 1 ;  determine  the  divisor  and  dividend  ? 

Ans.  165  and  15. 

60.  The  product  of  two  numbers  is  120,  and  if  you  add  4  to 
the  less,  the  product  will  be  168 ;  what  are  the  two  numbers? 

Ans.  12  and  10. 

61.  The  quotient  of  two  numbers  is  18,  and  their  sum  1,121; 
find  the  numbers?  Ans.  1,062  and  59. 

62.  Divide  256  into  two  such  parts,  that  their  quotient  will  be 
31 8  Ans.  248  and  8. 

63.  The  quotient  of  two  numbers  is  u7  and  their  difference  684; 
determine  the  numbers  ?  Ans.  703  and  19. 

64.  Divide  a  number  into  two  such  parts  that  their  ditFerence 
be  240  and  their  quotient  31  ?  Ans.  248  and  8. 

65.  With  1,350  shillings  I  paid  75  labourers  who  worked  during 
a  week;  how  paany  would  I  pay  with  1,836  shillings.     Ans.  102. 

66.  If  I  had  $350  more  my  stock  would  be  tripled ;  what  do  I 
possess?  Ans.  ^175. 

6  7.  The  sum  of  two  numbers  is  4,545,  and  one  of  them  is  4 
times  greater  than  the  other ;  what  are  the  numbers  ? 

Ans.  3,636  and  909. 


\ 


68. 

5,939, 
the  twc 

69. 
part  of 
parts  ? 

70.  ] 
first  ma 
24  mor 

71.  I 
more,  I 

72.  I 
divided 

73.  ^ 
give  2,7 

74.  1 
the  prod 
bers? 

75.  I 
it  by  12, 

76. 
their  pro 

77.  T 
determin 

78.  V\ 
as  456  b 

79.  A 
scribes  fo 
come;  to 
ment? 

80.  Tl 
second  is 

81.  Th 
their  sum 

82.  Th 
their  diflfei 

83.  Di' 
to  the  qui 

84.  A 
Jn  takinof 

o 


A  COLLECTION  OP  QUESTIONS.  185 

-  o^QQ  II  ^""^  ^^'^.^  M^  ?"^  ^"^^^^^  *^^  """^^'^  whose  sum  is 
o  939,  the  quotient  will  be  12  and  the  remainder  11  ;  what  are 

■         fiQ^'n-TTnnw     .  ^n..  456  and  5,483. 

69  Divide  100  into  two  parts  in  such  sort  that  the  seventh 
part  of  the  sextuple  of  one  of  the  parts  may  equal  24-;  what  are  the 

70.  Divide  the  number  92  into  4  parts,  in  such  sort  that  the 
fi^t  may  be  10  more  than  the  second,  18  more  than  the  third,  and 
24  more  than  the  fourth  ?  Ans.  36,  26,  18,  12. 

71.  It  1  had  three  times  more  money  than  I  have,  and  $245 
more,  I  would  have  $2,045  ;  what  have  I  ?  Ans.  $450. 

A-  -I'/k  \'  ^^^"^y  I  have  was  multiplied  by  8  and  the  product 
divided  by  7,  I  would  have  $24.  Ans  $21 

J.^  llltZtu  ^''""^  '^^'^  ^  ^^'  "^^^^  part  of  2,457  would 
give  J,731  tor  total?  ^^^  2 453 

74.  The  product  of  two  numbers  is  144,  and  the  sixth  part'of 
^e^product  IS  equal  to  three  times  the  less ;  what  are  the  2  nura- 

'Jk    T  ^     1,1  J  1  ^^*'  18  and  8. 

75    I  doubled  a  number  and  divided  it  by  4,  then  I  multiplied 
It  by  12,  and  the  third  of  the  result  was  48  ;  what  is  the  number? 

76.  One  of  the  factors  of  a  number  'is  37,  and  5  times 
their  product  is  10,730  ;  what  is  the  other  ?  Ans  58 

77.  The  sum  of  two  numbei-s  is  374,  and  their  quotient  is  21 ; 
determine  the  numbers  ?  ^W5  357  and  17 

oa  A^A  f  ^^^  "^°^ber  multiplied  by  12  will  give  the  same  product 
as  40h  by  16^  ^^^  ^^/^^ 

79.  A  person  having  445  shillings  per  month  to  si  id,  sib- 
scnbes  for  3  160  shillings  in  effects,  that  he  must  pay  out  of  his  in^ 
come;  to  what  must  he  reduce  his  expenses  to  fulfil  his  eno-a^e- 

"''«o   Ti     ..w..  ■         ^^^- 6  shillings  per  dJy^ 

80  Ihe  total  of  three  numbers  is  131,  the  third  is  89,  and  the 
second  is  quintuple  the  first ;  what  are  the  numbers  ? 

81.  The  less  of  two  numbers  is  7  more  than  their  difference,  and 
Uieir  sum  is  41 ;  what  are  the  numbers  ?  Ans.  16  and  25 

*}.^^'aI^'^  ^^^'""^  ^"^^  numbers  is  12,  and  by  tripling  their  sum, 
tneir  difference  IS  51;  what  is  the  greater?  ^k5.  29. 

°".  Divide  20  into  two  parts  in^such  sort  that  one  part  added 
3  quintuple  of  the  other  will  make  84  ?         Ans.  10  and  4. 

»4.  A  certain  person  wishing  to  buy  some  oranges,  finds  that 
ffl  taking  24  he  would  have  7id. over,  and  in  taking  30  he  would  " 


to 


jrao 


A   COLLKCTIOK    OF   QUBBTIONS. 


want  10^(1.  more; required  the  price  of  the  oranges  and  the  raone? 
the  person  had  ? 

Ans.  3d.  each  orange ;  68.  I^d.  the  money  the  person  had. 

85.  The  sum  of  two  numbers  is  460  and  the  less  is  equal  to 
their  difference;  what  are  they?  Ans.  150  and  300. 

86.  A  father  has  six  sons,  there  are  4  years  difference  between 
their  ages,  and  the  eldest  is  three  times  the  age  of  the  youngest  • 
what  is  the  age  of  each  ?  Ans.  14,  18,  22  and  26  yeaT^. 

87.  Two  gamblers  play  a  game  :  the  first  has  54  shillings,  the 
aecond  41.  After  the  game,  the  first  has  four  times  as  much  mone^ 
as  his  comrade ;  how  much  did  the  second  lose  ? 

Ans.  22  shillings. 

88.  Which  is  the  greater  of  two  numbers  of  which  the  less  is 
three,  and  the  sum  added  to  the  product  is  39  ?  Ans.  9. 

89.  Which  are  the  two  numbers  wliose  diflference  is  6,  and  of 
which  3  times  the  less  and  5  times  the  greater  mak«^  54  ? 

Ans.  3  and  9. 

90.  What  two  numbers  give  116  for  sum,  and  for  difference 
double  the  less?  Ans.  29  and  87. 

91.  The  sixth  part  of  9  times  the  sum  that  I  have,  divided  by 
three  and  sextupled,  gives  a  result  such  that  its  fifteenth  part  is 
30 ;  what  is  that  sum  ?  ^ns.  150. 

92.  A  gambler  being  asked  how  many  pounds  he  had,  answered : 
the  quotient  of  5  times  their  number,  divided  by  7,  being  multiplied 
by  13,  gives  a  product  equal  to  65  ;  how  many  had  he  ? 

Ans.  £1. 

93.  The  seventh  part  of  a  number,  multiplied  by  3,  augmented 
4,  and  divided  by  13  gives  4  for  quotient;  what  is  that  number? 

Ans.  112. 

94.  If  I  add  $10  to  four  times  the  triple  of  six  times  the  sum  I 
have,  I  will  have  $658  ;  how  m^ny  had  I  ?  Ans.  $9. 


FRACTIONS. 

95.  The  sum  of  two  fractions  is  f  and  their  difference  is  /y ; 
what  are  the  fractions  ?  Ans.  j\  and  f  f . 

96.  What  is  the  number  whose  difference  between  its  third  and 


its  fourth  part  is  16  ? 


Ans.  192. 


nt7 


^x7u„i. V-. 


!n   j:n?- 


TT  u»t.  xiuiuuur  wiii  uiuer  ujgui  iruui  lis  ^  anu  lis  f  j 


9 


Ans.  20. 


98.  With  3^  more,  the  |  and  the  ^  of  a  number  would  be 


equal ;  what  is  it  ? 


Ans.  28. 


A   COLLECTION    OF   QUESTIONS. 


187 


99   There  is  12^^  difference  between  the  fifth  and  the  ninth 
part  of  a  number  ;  what  is  it  ?  Ans  136 

100.  The  sum  of  two  numbers  is  20,  and  after  subtracting  i 

numbe"?  ''  ''  '^'  '''^"'  '^'^  '''  ^^"^^5  ^^at  are  llfos! 

ini    !?•  J  ,         ,  Ans.  8  and  12. 

101.  Pmd  a  number  whose  i  will  bo  equal  to  |  of  14? 

1  T:\  ^^^'T  ^'^*.7  .^^^'''  '^^'  ^y  «'^^'  tlie  first  is  eqS  t^lf  iho 
^  c^^the  other,  which  13  156  feet  higher;  what  is  the^.eight  of 

1U3.  Ihe  ^  and  -}  of  a  ship  are  under  water,  and  there  remains 
4  f-tovc.  water ;  what  is  its  depth  ?  Ans.  48  feet. 

104.  llie  i  and  J.  of  a  number  make  17^ ;  what  is  it? 

1  '^IhfjX  ^^'^  u^  f  ^^  ^  "^^^'''  *^  '^  ^'^'^^^  ^^'^  tofaTwm'be 
1 ;  what  is  the  number  ?  A      ± 

106.  A  number  is  such  that  if  you  add  1    i   i    of  t]m\^^r^c. 
number,  the  total  will  be  12,  &nAatnlZA'  *'  l^'llT 

107.  Find  a  number  whose  i,  i  and  ^  make  4J  ? 

Is  tKerJ™  ""'"^"  °°'  ''  "i'  '-""l  '''^■^  1"««™'  i«  i  '  "l^" 
whitt  il^  ^''^^^'  ""^  ""  "'''"^^'  multiplied  by  I  is  equal  t^li ; 

110.  If  the  triple  of  f  be  added  to  its  third,  the  whole  wilfbe 
115;  what  is  It?  ^^^  ^^ 

111.  After  selling  the  f  of  a  piece  of  cloth  there  remains  i*of 
the  piece  plus  6  yards ;  how  many  yards  did  it  contain  ? 

110    ^ru    ,    1      ,     <.  ^^*-  18My<is. 

fi,    i    /u    ^  "^       3  of  a  number  diminished  64  give  for  result 
tne  ^  ot  the  same  number ;  what  is  the  number  ?        Arts.  168. 

113.  j\  plus  ^  of  a  number  augmented  3,  give  for  result  half 
ot  the  same  number;  what  is  that  number  ?  Ans.  15. 

114.  The  f  and  i  of  a  number  and  twelve  more  make  iust 
aouWo  that  number ;  what  is  it  ?  Ans  32 

115.  If  I  had  i  1  and  |  of  what  I  have,  I  would  have*$150 
more  ;  how  many  have  I  ?  Ans.  $360. 

^iib.  ^-Aome^body  said :  if  I  had  the  |  and  1  of  the  double  of 
Wiiat  X  have,  I  would  have  |o  more ;  how  many  had  he  ? 

117.  The  f  plus  tV  of  the  sum  I  hiive,  plus  $29,  exceed  that 
same  sum  by  $5  ;  what  is  that  sum  I  Ans.  $160, 


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23  WEST  MAIN  STREET 

WEBSTER,  N.Y.  14580 

(716)  872-4503 


188 


A    COLLECTION    07   QUESTIONS. 


118.  A  iDd  is  divided  in  such  sort  that  the  |  is  white,  J  black, 
I  blue  and  the  remaining  12  feet  are  red;  what  is  the  length  of 
the  rod  ?  Ans.  49yV  ^Q®*« 

119.  I  bought  a  property,  and  paid  by  account  the  |  of  |  of  | 
of  the  price,  and  I  owe  yet  $60,635 ;  what  did  it  cost  ? 

Ans.  $109,143. 

120.  Divide  5  into  two  such  parts  that  the  quotient  of  greater 
by  the  less  will  be  also  5  ?  Ans.  |  and  4|. 

121.  With  the  money  I  have  I  wouW  pay  |  of  my  debts ;  with 
$1,000  more  I  would  acquit  myself  entirely  and  have  $200  over; 

'  how  much  have  I  ?     How  much  do  I  owe  ? 

Ans.  $400  and  $1,200. 

122.  The  third  of  my  money  exceeds  the  y*y  by  $35  ;  what  do 
I  possess?  Ans.  $1,050. 

123.  A  number  is  such  that  in  multiplying  its  fifth  by  its  sev- 
enth, it  is  lessened  one-fourth ;  what  is  it  ?  Ans.  2Q\, 

124.  If  you  subtract  -^  from  a  number,  1964  will  be  the  rem. ; 
what  is  it?  ^ws.  3,437. 

125.  The  I  of  f  of  a  number  augmented  J  of  |  will  make  11 ; 
what  is  it?  Ans.  12. 

126.  Determine  a  number  whose  i  of  |  taken  from  the  |  of  its 
I  will  give  unity  for  remainder.  Ans.  6/^. 

12*7.  An  article  which  cost  4,395  shillings  was  yold  for  two- 
third  of  five  times  what  it  cost ;  what  was  the  gain  ? 

Ans.  10,255  shillings. 

128.  Determine  a  number  such  that,  if  you  multiply  it  by  | 
and  divide  the  product  by  4^,  the  quotient  will  be  16  2 

Ans.  96. 

129.  The  fifth  part  of  the  sum  I  have  is  equal  to  the  same  sum 
diminished  $20 ;  what  have  I  ?  Ans.  $25. 

130.  AVhat  number  must  be  added  to  the  f  and  the  i  of  32  to 
give  671  for  sum  ?  Ans.  15i. 

131.  A  certain  person  said :  I  have  spent  the  |  of  the  |  of  what 
I  had,  and  I  have  yet  $10 ;  how  many  had  he  1  Ans.  $20. 

132.  If  I  had  $30  more,  I  would  pav  my  debts ;  $20  Ifess,  I 
would  pay  but  the  | ;  how  much  money  have  I  ?  How  much  do 
I  owe  ?  Ans.  $45  and  $75. 

133.  What  sum  must  be  subtracted  from  the  4  and  the  \  of 

134    The  sum  of  two  numbers  is,  5,760,  and  their  difference  is 

hat  are  the  two  numbers  ? 


equal  to  the  third  of  the  greater : 


Ans.  3,466  and  2,304. 


^sS.. 


A   COLLECTION   OP   QUESTIONS. 


},  }  black, 
length  of 
j\  f(Qet. 
of  f  of  f 

09,143. 
of  greater 
and  4^^. 
ibts;  with 
200  over ; 

$:,200. 
;  what  do 
$1,050. 
by  its  sev' 
as.  26^. 
the  rem. ; 
.  3,437. 
make  11 ; 
ins.  12. 
be  I  of  its 
ns.  6^j. 
I  for  two- 
hillings, 
[y  it  by  I 

Arts.  96. 
same  sum 
ns.  $25. 
i  of  32  to 
ns.  15^. 
}  I  of  what 
ns.  $20. 
$20  Iftss,  I 
w  much  do 
md$76. 
id  the  ^  of 

A/no    A  A 

lifference  is 
ibers? 
d  2)304. 


189 


135.  By  what  number  must  you  multiply  a  sum  to  lessen  it  |  ? 

T>      \.  ^^^'  i' 

136.  By  what  number  must  you  divide  a  sum  to  render  it  once 
and  a  half  greater  ?  j^^g   a 

^    137.  Of  three  fractions  the  second  is  double  the  first,  the' third 
IS  f ,  and  their  sum  is  ^  ;  what  are  the  two  first  fractions  ? 

/ins    1_  a.Tifl  _i_ 

138.  To  double  a  number  you  must  multiply  its  V  by  its  ninth 
prfrt ;  what  is  it  ?  ^^^  27. 

,  ]^^:J^^  3  .of  one  number  is   equal  to  the  a  of  another,  and 
their  difference  is  6 ;  determine  those  two  numbers  ?  Ans.  18  and  12 

140.  The  sum  of  two  numbers  is  4,  and  the  quotient  of  the  less 
by  the  grc^ater  is  4  ;  what  are  they  ?  Ans.  2i  and  la. 

141.  Divide  60  into  two  such  parts  that  the  I  of  one  may  be 
equal  to  }  of  the  other  ?  Ans.  32  and  28. 

142.  The  father  and  son  together  are  70  years  old,  the  age  of 
the  father  multiplied  by  3  is  equal  to  the  son's  age  multiplied  by 
1i  ;  what  are  the  ages  ?  Ans.  20  and  50 

143.  A  greyhound  starts  after  a  hare  that  is  82  leaps  ahead- 
while  the  greyhound  makes  9  leaps  the  hare  makes  13,  but  3  leaps 
of  the  greyhound  are  equal  to  5  leaps  of  the  hare ;  how  many 
leaps  must  the  greyhound  make  to  catch  the  hare  ? 

144.  A  watch  marks  12,  and  both  hands  are  together ;  required 
on  what  part  of  the  dial  they  will  next  meet  ? 

,  _    _  .   .  -^^5.  1  o'clock  5/p  minutes. 

145.  It  is  just  six  0  clock ;  when  will  the  hands  meet  ? 

.  ^W5.  3 2y»y  minutes  past  6. 

146.  It  IS  just  twelve ;  required  how  many  tidies  the  hands  shall 
mffet  from  twelve  till  midnight,  and  at  what  o'clock  each  time? 

Ans. 

147.  The  f  and  J  of  a  number  make  39 ;  what  is  that  number  f 

■     ._     .  •  ^ns.  60. 

148.  A  man  can  do  a  piece  of  work  in  ^  day,  his  wife  could  do 
the  same  in  1,  and  their  son  in  ij  day ;  what  time  would  the  three 
together  take  to  do  it  ?  Ans.  ■*-  day. 

149.  A  spring  would  fill  a  basin  in  3  hours,  another  would  fill  it 
in  fi  V,^««, .   if  f^e  t^Q  j.^jj  together,  required  in  what  time  thov 


would  fill  it? 


Ans.  11  hour. 


150.  A  pump  would  empty  a  ditch  in  8^  days,  another  would 
empty  it  in  7f ;   if  both  work  together,  in  what  time  will  the  ditch 


1 


be  dry! 


Ans.  3|f  f  dsjm. 


w> 


A   COLLECTION   OF   QUESTIONS. 


161.  A  set  of  workmen  can  build  a  wall  45  yards  long  in  0 
days  by  working  9  hourtj  per  day ;  another  set  would  build  it  in 
8  days  by  working  7  hours  per  day :  if  both  work  together  and 
work  8  hours  a  day,  in  how  many  days  will  the  wall  be  built  ? 

Am.  21  hours +tV7>  ^^  ^  ^^J^  ^  hours +  //,. 

152  Two  bands  of  reapers  can  reap  a  field :  the  first  in  4  days, 
and  the  second  in  6  days ;  if  J  the  first  and  I  of  the  second  be 
employed,  in  what  time  will  the  field  be  reaped  ? 

Ans.  5^^  days. 

153.  A  cock  gives  8  gallons  of  water  in  1  minutes,  another 
6  gallons  in  6  minutes ;  how  many  gallons  do  both  give  in  one 
minute  ?  Ans.  l^i  gallons. 

164.  A  person  questioned  about  his  age  answei-ed :  the  f  and 
the  ]•  of  my  age  plus  7  years,  just  make  my  age  3  years  hence  ; 
what  is  his  age  ?  Ans.  30  years. 

155.  The  double  of  a  sum  augmented  i,  }  and  }  of  the  same 
jwim  and  $5  more  make  $76 ;  what  is  that  sum  ?         Ans.  #24. 

156.  A  water-spout  would  fill  a  basin  in  }  hour;  another  would 
do  the  same  in  |  hour ;  and  a  third  in  |  hour ;  in  what  tima 
would  the  three  running  together  fill  it  ? 

Ans.  ^V  Jio^i*  OJ*  3  minutes. 

157.  I  can  do  a  piece  of  work  in  4  days ;  my  brother  can  do 
the  same  in  5  days ;  if  we  both  work  together,  in  v/hat  time  will 
it  be  done  ?  ^ns.  2|  days. 

158.  A  set  of  workmen  can  sink  a  well  in  9  days,  another  can 
do  it  in  10  days,  and  a  third  in  12  days ;  now  if  I  employ  \  of  the 
first  band,  |  of  the  second,  and  J  of  the  third,  in  what  time  will 
the  well  be  dug  out  ?  Ans.  9|^  days. 

159.  A  basin  has  three  cocks :  two  destined  to  fill  it,  and  a  third 
to  empty  it  The'first  cock  would  fill  the  basin  alone  in  4  hottts, 
the  second  in  three  hours,  and  the  third  would  empty  it  in  6  hours ; 
now  if  the  three  be  opened  together,  in  what  time  will  it  be  filled? 

Ans.  2 1  hours. 

160.  A  basin  has  three  cocks  :  two  to  fill,  and  one  to  empty  it. 
The  first  would  fill  it  alone  in  4  hours,  the  second  in  5  hours,  and 
the  thii-d  would  empty  it  in  2  hours.  The  basin  being  already 
full,  the  three  cocks  are  opened  together ;  in  what  time  will  it  bo 
ompty  ?  ^w«.  20  hours. 

161.  A  workman  can  do  a  piece  of  work  in  |  day,  another  can 
do  it  in  f  day ;  if  the  two  work  together,  in  what  time  will  it  bo 
done  ?  ^ws.  \{  day. 

lar.  A  mother  divides  a  certain  number  of  sugar-plums  between 


A   COLLECTION   OP   QUESTIONS. 


191 


her  three  daughters ;  the  youngest  receives  the  f  of  the  whole,  the 
second  l,  and  the  third  12  for  her  part;  how  many  were  there,  and 
what  was  the  part  of  each  ? 

-  _„    -,,  ^ns.  Total  45  ;  12,  15,  18,  respectively. 

163.  Ihe  f  and  the  i-  of  what  I  have  in  my  purse,  with  $10 
more,  would  make  $0  more  than  I  have ;  what  does  the  purse 
contam  ?  ^^^  ^§q^ 

164.  The  triple  of  a  sum  added  to  the  i  and  \  of  the  same  su'ra, 
and  $6,000  more,  would  make  $22,200  ;  what  is  that  sum  ? 

IflR     rp,       ,..r  ^ws.  14,800. 

169.  liie  difference  between  the  |  and  the  f  of  a  number  is 
12  ;  what  is  that  number  ?  ^^^^  216. 

166.  The  total  of  the  f  and  the  f  of  a  number,  diminished  the 
f  of  the  same  number  gives  14 ;  what  is  the  number  ? 

, -H    m  ,  .  ^**^-  24. 

157.  Iwo  cocks  running  togethijr  would  fill  a  basin  in  2  hours  • 
one  alone  would  fiM  It  in  5  :  in  what  time  would  the  other  SIl  it  if 


it  were  to  run  alone  / 


Ans.  31  hours. 


168.  I  spent  the  |  of  what  I  had  in  my  purse,  and  if  I  add  $44 
to  what  remains,  the  sum  it  contained  first  will  be  auo-mented  i  • 
what  did  it  contain  ?  ^^^.^  $48 

169.  One  cock  runs  11  gallons  in  8  minutes,  another  runs  7 
gallons  m  5  minutes ;  which  runs  the  most  ? 

Ans.  The  second,  by  ^V  gal.  per  min. 

170.  A  basm  receives  45f  gallons  of  water  per  hour  by  a  cock 
and  leaks  by  a  hole  37f  gallons ;  how  many  gallons  does  it  retain 
P^^,;^^"^';  .  A71S.  7fi  gallons. 

171.  A  certain  person  not  recollecting  what  he  paid  for  an  arti- 
cle only  remembers  that  there  were  $14  difference  between  the  J 
and  the  |  of  the  price ;  what  is  it  ?  '      Ans.  $40. 

_  172.  The  f  of  a  number  diminished  the  |  of  the  same  number 
gives  18  for  rem. ;  what  is  that  number  i  Ans.  70. 

173.  The  sum  of  the  f  and  the  j\  of  a  number  less  one-half  of 
the  same  number,  gives  24  ;  what  is  that  number  ?        Ans.  40. 

174.  Two  workmen  can  do  a  piece  of  work  in  3  hours,  one  alone 
can  do  it  in  7  hours  ;  in  what  time  will  the  other  do  it  alone  ? 

.  ^«*.  5:J:  hours. 

175.  Ihree  cocks  running  together  would  fill  a  basin  in  4  hours; 
one  of  them  would  fill  it  alone  in  10  hours,  another  would  fill  it  in 
12  hours ;  what  time  would  the  third  running  alone  take  to  fill 

.ifVr  ^"^'  15  hours. 

176.  Ihe  quarter  of  a  field  is  sown  with  wheat,  the  ^  with  barley 


1 


192 


A    COLLECTION    OP    QUESTIONS. 


and  the  remainder  with  oats.  The  portion  sown  with  barley  con- 
tains 10  acres  more  than  that  sown  with  wheat;  required  the  ex- 
tent of  the  whole  field  and  that  of  each  part  1 

Ans.  Whole  extent  56  acres;  14  wheat,  24  barley,  18  oats. 
1*77.  I  have  already  sold  the  |  of  a  basket  of  eggs,  and  if  I  add 
39  eggs  to  what  remains,  the  primitive  value  of  the  basket  will  be 
augmented  one-half,  how  many  eggs  were  there  in  the  basket  ? 

Ans.  30. 

178.  A  steam-loom  weaves  5  yards  of  cloth  in  3  houre,  another 
1 2  yds.  in  7  hours  ;  which  has  the  greater  power  ?  ^ 

Ans.  The  latter  weaves  ^  yd.  per 
hour  more  than  the  former. 

179.  A  ribbon  was  cut  into  5  parts  of  f  yd.  each ;  what  was  its 
length?  Ans.  1}  yd. 

180.  A  tradesman  can  do  a  piece  of  work  in  5|  days  ;  in  what 
time  will  he  do  the  |  of  the  work  ?  Ans.  4|f  days. 

181.  A  ship  sails  at  the  rate  of  16^  miles  an  hour;  how  many 
miles  will  she  sail  in  3-^  hours  ?  Ans.  63y\  miles. 

182.  A  weaver  weaves  7  yards  of  linen  in  8  hours;  how  many 
yards  will  he  weave  in  4|  hours  ?  Ans.  4i|-  yds. 

183.  A  man  weaves  7  yards  of  linen  in  8  hours;  what  time  will 
he  take  to  weave  4f  yds.  ?  Ans.  5if  hours. 

184.  If  5  gallons  of  wine  be  mixed  with  7  gallons  of  water ;  re- 
quired what  quantity  of  water  in  |  gallon  of  the  mixture  'i 

Ans.  if  gallon  of  wine  f  |-  of  water. 

185.  If  the  f  of  the  f  of  a  number  make  120,  what  is  it  ? 

Ans.  162. 

186.  A  person  being  asked  the  time  of  day  answered ;  it  is  the  f 
off  of  I  of  24  hours ;  what  o'clock  was  it  ?        Ans.  10  o'clock. 

187.  Divide  a  succession  between  three  heirs  in  such  sort  that 
the  first  may  have  the  ^  of  the  whole,  and  the  second  the  ^  of 
the  remainder ;  what  is  the  part  of  each  ? 

Ans.  First  ^,  second  /y,  and  the  third  ■^. 

188.  A  sum  of  money  was  employed  in  four  successive  pur- 
chases. For  the  first  purchase  the  |  of  the  sum  was  laid  out ;  for 
the  second,  ^  of  the  remainder  ;  foi;  the  third,  the  f  of  the  second 
remainder ;  and  finally,  for  the  fourth  the  last  remainder,  which 
was  $5 ;  required  the  total  sum,  and  the  amount  of  each  pur- 
chase ? 

Ans.  Total  $50  ;  first  f ,  second,  ^y,  third  -^^y,  fourth  yV* 

189.  A  certain  person  leaves  to  his  nephew  a  fortune  of  $80,000, 
and  orders  the  ^  of  f  of  the  succession  to  be  given  to  a  servant, 


A   COLLECTION   OF   aUESTIONS. 


193 


and  to  his  nurse  ]■  of  |  of  i  of  the  same  succession ;  what  is  the 
portion  of  each  ?  ' 

.if     ,^^%^.,f  *  ^^  t^e  l^^gth  of  a  garden  is  48  yards ;  what  is 
the  length  of  It?  ^n..  90  yards. 

.u  ;  .1*     ^'T  '''^^^''  "l'"^^*^^  ^^^^^"  themselves  a  sum  of  money 
that  they  had  stolen ;  the  first  takes  the  f  of  it,  and  the  two  othei^ 
take  each  half  of  what  remamed ;  what  part  fell  to  each  robber  ? 
Ans.  First  f  of  the  sum,  and  the  two  others  j\  each. 

192.  A  stage  performs  a  journey  in  four  days.  The  first  day  it 
tj-avels  the  i  of  the  whole  route ;  the  second  day  it  travels  the  i 
of  the  remainder;  the  third  day  it  travels  the  ^  of  the  second  re- 
mainder ;  and  lastly,  the  fourth  day  it  completes  the  journey  and 
goes  144  miles;  required  the  length  of  the  journey,  and  each  day^s 
travelling  ?  .  •'  j 

Ans.  Length  540  miles ;  first  day  108  miles, 
and  each  of  the  other  days  144  miles. 

193.  A  tradesman  can  finish  a  piece  of  work  in  |  of  a  day  an- 
other can  do  the. same  in  a  day  :  1st.  What  time  will  they  take  to 
do  It  together  ?  2d.  What  part  of  the  work  will  be  done  by  each  ? 
8d.  What  will  be  the  gain  of  each,  if  the  whole  be  worth  4s  7d  ? 

Ans.  1st.,  r\  day ;   2d.,  the  1st.  ^V  of  the  work,  the  2d.' 
the  Jy ;  3d.,  the  1st.  will  have  2s.  6d.,  the  2d.  2s.  Id. 

194.  A  little  boy  playing  marbles  augmented  his  number  x  the 
hrst  day ;  on  the  next  day  he  augmented  his  last  number  i ;  finally 
he  plays  a  third  day,  and  augments  his  last  number  f ,  and  finds 
lumselt  master  of  63  marbles ;  how  many  had  he  when  he  beffan 

^  ^^^y  •  Ans.  21, 

195.  What  number  multiplied  by  3|  will  give  1  for  product! 

Affis  -A- 

196.  In  8  hours  5f  yards  are  woven,  in  what  time  will  Vyard 
be  woven  ?  j^^^  j/ 

197.  A  ship  sails  at  the  rate  of  29f  miles  in  3f  hours'  whit  is 
that  per  hour?  An..  8^^  miles  per  hour. 

lUb.  vyiule  a  locomotive  runs  the  whole  route,  a  stage  runs  but 
the  y3j-of  it ;  how  many  times  does  the  locomotive  go  quicker  than 
the  stage  ?_      _  An*.  Slimes  quicker. 

199.  A  ship  IS  victualled  for  12  days  only;  and  must  be  kept 
on  sea  during  IS  days;  to  what  must  the  daily  rations  of  each 
man  be  reduced  ?  Jlw*.  f  of  one.    ■. 

200.  Four  labourers  work  together  and  are  paid  equally.  Now 
the  first  who  worked  the  whole  day  received  4s.  2d.  while  the 


194 


A  OOIXBCnON  OP  auESTioira. 


second  received  bnt  38.  4d.,  the  third  2s.  6d.,  and  the  fourth  Is.  8d. 
Required  what  part  of  the  day  the  three  last  labourers  worked  ? 

Alls.  The  second  f  day,  3rd  |,  4th  |  day. 
2Q1.  A  spinning-wheel  takes  in  1|^  yard  of  thread  every  ti^rn  it 
makes ;  how  many  turns  should  it  make  to  wind  up  45f  yards  ? 

Ans.  40^J^  turns. 

202.  An  omnibus  takes  ^  hour  to  reach  its  destination,  it  sta- 
tions ^  hour,  and  takes  ^  hour  to  return  to  its  starting  place. 
Admitting  that  a  trip  is  composed  of  going  to  and  from  the 
station;  how  many  such  trips  will  the  omnibus  perform  from 
half-past  seven  in  the  morning  till  10  o'clock  at  night? 

Ans.  14^  trips. 

203.  A  traveller  having  missed  the  stage,  it  is  already  29  miles 
a<head  of  him.  Ho  then  takes  a  calash  that  goes  at  the ,  rate  of 
9  miles  an  hour,  the  stage  traveUing  out  5\  miles  per  hour.  In 
what  time  will  the  calash  overtake  the  stage  ? 

Ans.  7  hours  44  minutes. 

204.  There  is  29  miles  distance  between  two  towns.  Two  car- 
riages start,  one  from  each  town  and  run  towards  each  other,  the 
first  goes  at  the  rate  of  9  miles  per  hour,  and  the  second  5^  milas 
per  hour ;  in  what  time  will  the  carriages  meet,  and  what  will  bo 
the  distance  performed  by  each  ? 

Ans.  2-^  hours.     One  18i|  miles,  other  10|^  miles. 

205.  Two  carriages  travel  at  the  rate  of  9  miles  and  5^  miles 
respectively,  start  together  from  the  same  town  to  reach  the  neigh- 
bouring town  distant  29  miles.  In  what  time  will  the  former 
Mfrive  before  the  latter?  ^rw.  2-i5/^  hours. 

206.  A  saloon  requires  8^  pieces  of  wall-paper  f  yard  wide  to 
line  it.     How  many  pieces  ^  yard  wide  would  do  the  same  ? 

Ans.  12f. 

207.  A  spring  runs  8|  gallons  of  water  in  6  minutes ;  in  what 
time  will  it  run  a  gallon  ?  Ans.  4  minute. 

208.  A  weaver  weaves  9|  yards  of  cloth  in  2f  days ;  how  many 
yards  does  he  weave  per  day  ?  Ans.  3||. 

209.  I  sold  the  ^  of  a  piece  of  cloth  and  there  remains  yet  15 
yards ;  what  was  the  length  of  the  piece? 

Ans.  35  yards. 

210.  A  bale  of  merchandise  was  sold  for  $75 ;  if  it  had  been 
sold  for  $9  more,  %Tie>  pront  would  have  been  just  |  of  the  uiss 
cost ;  what  did  it  cost  ?  Ans.  $60. 

21  i.  The  rail  oars  start  from  New  York  at  noon  and  arrive  at 
Philadelphia  at  4  o'clock  P.  M.    A  stage  started  with  the  cars,  and 


A  COLLECTION   OP   UUBSTI0N8. 


m 


went  but  the  I  of  the  route :  at  what  o'clock  will  the  stage  arrive 

ot   ^^&^  •  t'  ^'  -^^^-  ^^^^  ^^y  at  2  o'clock  A.  M. 

212.  While  a  horseman  goes  the  f  of  a  journey  a  footman  can 
only  travel  the  j^ ;  how  many  times  does  the  horseman  go  quicker 

I,  n  .no  ^,*'™^  .^I^'"  ^"^"^  water-spouts  take  to  fill  a  basin  that 
holds  508  gallons,  if  one  runs  5^  gallons  per  minute,  and  the 
other  4A  gallons.  ^^^,.  48  minutes. 

J 14.  A  garrison  has  provisions  for  9  days  only,  and  must  hold 
out  tor  12  days :  to  what  fraction  must  the  daily  rations  of  each 
m^  be  reduced?  ^r...  to  |  of  usual. 

-*lt).  A  watch  is  now  regular,  gets  out  of  order  and  advances  5* 
mmutes  in  a  day ;  m  how  many  days  will  it  again  mark  the  exact 

Ti«    TK  •.  u     ,  ^w«.  130if  days. 

216.  Ihree  writers  equally  clever  can  write  40  pages  each  per 
day ;  now  if  the  first  write  but  30  pages,  the  second  25,  and  tiio 
tnird  20 :  required  during  what  portion  of  the  day  each  worked? 

oi'r    T4.     u    ,    .  .  .         ,         •^'*^-  ^^^'  ^'  ^'^^'  ^'  3rd  i  day. 

^17.  It  a  bucket  takes  1^  minute  to  reach  the  bottom  of  a  well 
and  remains  i  minute  below,  then  If  minute  ascending,  how  many 
buckets  of  water  may  be  drawii  in  250  minutes. 

o,o    rp.  .  -^^-  "^2  buckets. 

-il8.  iwo  couriers  start  at  the  same  time  at  a  distance  of  92* 
miles  apart,  to  meet  emjh  other  and  travel;  the  first  7  miles  an  hour 
the  second  13^  miles  an  hour:  in  what  time  will  they  meet,  and 
what  will  be  the  distance  travelled  by  each  ? 

Ans.  In  4^  hours.     The  first  travelled 
31^  miles,  the  second  60^  miles. 

219.  A  fox  that  makes  2^  leaps  in  a  second  is  already  30f 
leaps  a-head,  when  a  dog.  that  makes  4^  leaps  in  a  second  starts 
after  him. ,  In  what  time  will  the  dog  overtake  the  fox  ? 

rton   rr  •  ^^^*  ^^A  seconds. 

220.  Iwo  couriers  start  at  the  same  time  from  the  same  place 
for  a  neighbouring  town  distant  92^  miles,  the  fii-st  travels  13^ 
miles  an  hour,  the  second  1  idem :  how  many  hours  will  the  first 
arrive  before  the  second  ?  Jns.  6^*  hours. 

221.  A  courier  goes  24  miles  in  2  hours.     Three  "hours  aft«r 
his  departure  another  starts  and  goes  12  miles  in  5  hours,  in  how   ' 
*«it>«ijr  iiuuio  \\fiit  illQ  laiwr  uveriake  ine  lonuer? 

ftor.   fxT. ,  -^^*'  15  hours. 

1^22.  With  13t  yards  of  old  silk  |  wide  I  can  line  a  vestment; 
now  many  yards  |  wide  will  do  the  same  ?       Ans.  12i|  yard«. 


106 


A    COLLECTION    OP   QUESTIONS. 


323.  There  is  a  levy  of  $800  to  be  taken  of  three  villages  in 
proportion  to  their  inhabitants,  in  the  first  there  are  240,  second 
510,  third  450  inhabitants:  what  share  of  the  impost  will  each 
have  to  pay  ?  Ans.  Ist.  $160,  2nd.  $340,  4th.  $300. 

224.  An  uncle  on  his  death-bed  bequeathes  to  his  three  nephews 
a  fortune  of  $67,500  in  proportion  to  their  age.  The  first  is  30, 
the  second  25,  the  third  20  years  of  age :  required  what  will  fall 
to  each?  Ans.  Ist.  $27,000,  2nd.  $22,600,  3rd.  $18,000. 

225.  Divide  the  number.  1,028  into  three  parts  so  that  they  bo 
between  themselves  as  the  three  fractions,  f,  |,  |  ? 

Ans.  320,  420,  288. 

226.  Divide  $450  between  three  persons  so  that  the  second  may 
have  the  f  of  the  first,  and  the  third  the  ^  of  what  the  two  first 
have  together?  Ans.  $200,  $150,  $100. 

227. '^Divide  100  shilHngs  between  two  persons,  and  give  the 
second  the  f  of  the  first?  Ans.  60,  40  shillings. 

228.  Divide  $180  between  two  persons,  and  give  the  second  i 
of  the  first's  part  more  than  the  first  ?  Ans.  $80,  $100. 

229.  Divide  |  into  two  parts  so  that  they  be  between  themselves 

as  4  and  7  ?  .  ^»»*-  H'  ^' 

230.  The  power  of  one  machine  is  to  that  of  another  as  6  is  to 
7,  while  one  makes  48  yards  of  work :  how  many  will  the  other 
-j^j^iQ  ?  ^^**  ^^  yards. 

231.  Distribute  $582  between  3  persons  so  that  the  part  of  the 
first  be  to  the  second  as  ^  is  to  |,  and  that  the  part  of  the  second 
be  to  that  of  the  third  as  f  is  to  ^J  ?        Ans.  $168,  $252,  $162. 

232.  What  is  the  superficies  of  a  rectangular  garden,  bemg  40 
yards  long  by  30  yards  in  breadth  ?  Ans.  1,200  yards. 

233.  What  is  the  area  of  a  meadow  in  the  form  a  triangle  of 
60  yards  of  base  and  48  in  height?        .         Ans.  1,440  yards. 

234.  What  is  the  area  of  a  yard  forming  a  trapezium  one  of 
whose  sides  is  34  yards  and  the  other  56,  its  height  being  2.5 
yaj.(jg^  u4w*.  1,125  yards. 

235.  What  is  the  area  of  a  rhombus,  whose  base  is  44yV  and 
height  38|  yards?  Ans.  I,7l6|f  yards. 

236.  What  is  the  superficies  of  a  pillar  17  yards  high  and  7 
yards  in  circumference?  •^'**'  l^^  yards. 

237..  The  circumference  of  a  cone  iV  12  yards,  and  the  distance 
irom  ine  summji  lo  mv  wjwc  w  w  jaiw3_,  n^^v  tt--v,.-.,  2- s 


of  it  cost  at  3  shillings  the  square  yard  ? 


Ans,  108  shillings. 


197 


A  Table  for  finding  the  Interest  of  any  sum  of  Moneu  for  «u- 
numher  of  months,  .eeks,  or  lays,  It  any  LuT^c^l  "*^ 


JQ  *.  d. 

0  0  Oi 

0  0  u 

0  0  2 

0  0  2i 

0  0  3i 

0  0  4 

0  0  4i 

0  0  54 

0  0  6 

0  0  6i 

0  1  14 

0  1  7| 

0  2  24 

0  2  9 

0  3  3i 

0  3  10 

0  4  4i 

0  4  114 
0  5  5| 

0  10  Hi 

0  16  54 

1  1  11 
1  7  4| 
1  12  lOi 

1  IB    44 

2  3  10 

2  9  3i 

2  14  9i 

7 

4i 
2 


•5  9 


8  4 
10  19 
13  13  Hi 
16  18  9 
19  3  6| 
21  18  44 
24  13  \l 
27  7  114 
54  15  lOi 
82  3  10 


y 


• 


198 


Rule.  Multiply  the  principal  by  the  rate  per  cent.,  and  the 
number  of  months,  weeks,  or  days,  which  are  required,  cut  off 
two  figures  on  the  right  hand  side  of  the  product,  and  collect  from 
the  table  the  several  sums  against  the  different  numbers,  which 
when  added,  will  make  the  number  remaining.  Add  the  several 
Bums  together,  and  it  will  give  the  interest  required. 

N.  B.  For  every  10  that  is  cut  off  in  months,  add  twopence ; 
for  every  10  cut  off  in  weeks,  add  a  half-penuy ;  and  for  every 
40  in  the  days,  1  farthing. 

EXAMPLES. 

1.  What  is  the  interest  of  £2467  lOs.  for  10  months,  at  4  per 

cent,  per  annum  ?  ^        ^    ^ 

2467  :  10  900=75  :    0  :  0 

4  80=  6  :  13  :  4 

, 7=  0  :  11  :  8 


9870  :    0 

10 
987100 


987=82  :    5:0 


2   What  is  the  interest  of  £2467  10s.  for  12  weeks,  at  5  per 

cent.!  2467:10        •  1000=19:    4:    7\ 

5  400=  7:13:10 

„  80=  1  :  10  :    H 

12337  :  10  50=  0  :    0  :    2^      ^ 


12 


1480150=28  :    9  :    5 


1480150  :    0 

3.  What  is  the  interest  of  £2467  lOe.,  50  days,  at  6  per  cent.! 
2467  :  10  7000=19  :  3  :    6^ 

6  400=  1  :  1  :  11 

•  —_— .  •  2=  0  :  0  :    U 

14805  :    0  50=  0  :  0  :    Oi 


60 


7402160=20  :  5  :    7 


7402150  :    0 
To  fiiid  what  an  Estate,  fnm  me  to  £60,000  per  a^nmm  will 

camB  to  for  one  day. 
Rule  1.  Collect  the  annual  rent  or  income  from  the  table  for 
1  year,  against  which  take  the  several  sums  for  one  day,  add 
them  together,  and  it  will  give  the  answer. 


109 


An  estate  of  £376  per  annum,  what  m  that  per  day  t 

300=0  :  16  :    5^ 

70=0  :    3  :  10 

6=0  :    0  :    4 


370=1  :    0  :  ,7^ 
To  find  the  amount  of  any  income,  salary,  or  servants'  wages^ 

for  any  number  of  months,  weeks,  or  days. 
Rule.   Multiply  the  yearly  income  or  salary  by  the  number 
of  months,  weeks,  or  days,  and  collect  the  product  from  the  table. 
What  will  £270  per  annum  come  to  for  11  months,  for  3  weeks, 
and  for  6  days? 


270 
11 

2970 


270 
6 

1620 


For  11  months, 
2000=166  :  13  :  4 
900=  75  :    0:0 


70= 


5 


16  :  8 


2970=247  :  10  :  0 

For  6  days. 
1000=2  :  14  :    9^ 
600=1  :  12  :  loj 
20=0  :    1  :    l| 

1620=4  :    8  :    9i 


For  3  weeks. 
270     300=15:    7:    8^ 
3       JK)=  0  :    3  :  loj 

810      =     15  :  11  :    6i 

For  the  whole  time. 
247  :  10  :  0 
15:  11  :  6i 
4  :    8  :  9i 


267  :  10  :  3| 


A   Table  showing  the  number  of  days  from  any  day  in  the 
mxmth  to  the  same  day  in  any  other  month,  through  the  year. 


FROM 


January 
February 
March 
April  . 
May  .  . 
June  . 
July .  . 
August 
Septembei 
October  . 
November 
December 


TO 


334 

306 

275 

245 

214 

184 

153 

12-2 

92 

61 

31 


4 

i 

1—5 
< 

^ 
S 

01 

a 

s 

1— 1 

9 

Aug. 

31 

59 

90 

120 

151 

ISl 

212 

365 

28 

59 

89 

120 

150 

181 

337 

365 

31 

61 

92 

122 

153 

306 

334 

365 

30 

61 

91 

122 

276 

304 

335 

365 

31 

61 

92 

245 

273 

304 

334 

365 

30 

61 

215 

243 

274 

304 

335 

365 

31 

184 

212 

243  273 

304 

335 

3fin 

153 

181 

•  212  242 

273 

303 

334 

123 

151 

182  212 

243 

273 

304 

92 

120 

151  181 

212  242 

273 

62 

90 

121 

151 

182 

212 

243 

243 
212 

184 

153 

123 

92 

62 

31 

365 

335 

304 

242 


u 
O 


273 

242 

214 

183 

153 

122 

92 

61 

30 

365 

334 

304 


> 
o 

25 


304 

273 

245 

214 

184 

153 

123 

92 

61 

31 

365 


334 
303 
275 
244 
214 
183 
153 
122 
91 
01 
30 


835|  365 


200 


A  COMPENDIUM   OF   BOOK-KEEPING. 

BY  SINGLE  ENTRY. 


Book-keeping  is  the  art  of  recording  the  transactions  of  persons 
in  business  so  as  to  exibit  a  state  of  their  affairs  in  a  concise 
and  satisfactory  manner. 

Books  may  be  kept  either  by  Single  or  by  Double  Entry ^  but 
Single  Entry  is  the  method  chiefly  used  in  retail  business. 

The  books  found  most  expedient  in  Single  Entry,  are  the  Day- 
Bookj  the  Cash-Book,  the  Ledger,  and  the  Bill-Book.       ** 

The  Day-Book  begins  with  an  account  of  the  trader's  property, 
debts,  (fee. ;  and  are  entered  in  the  order  of  their  occurrence,  the 
daily  transactions  of  goods  bought  and  sold. 

The  Cash-Book  is  a  register  of  all  money  transactions.  On  the 
left-hand  page,  Cash  is  made  Debtor  to  all  sums  received;  and 
on  the  right,  Cash  is  made  Creditor  by  all  sums  paid. 

The  Ledger  collects  together  the  scattered  accounts  in  the  Day- 
Book  and  Cash-Book,  and  places  the  Debtors  and  Creditors  upon 
opposite  pages  of  the  same  folio ;  and  a  reference  is  made  to  the 
folio  of  the  books  from  which .  the  respective  accounts  are  extrac- 
ted, by  figures  placed  in  a  column  against  the  sums.  References 
are  also  made  in  the  Day-Book  and  Cash-Book,  to  the  folios  in 
the  Ledger,  where  the  amounts  are  collected.  This  process  is 
called  posting,  and  the  following  general  rule  should  be  remem- 
bered by  the  learner,  when  engaged  in  transferring  the  register 
of  mercantile  proceedings  from  the  previous  books  to  the  Ledger : 

The  person  from  whom  you  purchase  goods,  or  from  whom 
you  receive  money,  is  Creditor  ;  and,  on  the  contrary,  the  person 
to  whom  you  sell  goods,  or  to  whom  you  pay  money,  is  Debtor, 

In  the  Bill-Book  are  inserted  the  particulars  of  all  Bills  of  Ex- 
change ;  and  it  is  sometimes  found  expedient  to  keep  for  this  pur- 
pose two  books,  into  one  of  which  are  copied  Bills  Receivable^ 
or  such  as  come  into  the  tradesman's  possession,  and  are 'drawn 
upon  some  other  person;  in  the  other  book  are  entered  Bills 
Payable,  which  are  those  that  are  drawn  upon  and  accepted  by 
the  tradesman  himself. 


201 


•    aMM^M 

DAY  BOOK. 

(foUo  1.) 

I 

o   »- 
O    V 

1 

1 
1 

1 

i 
2 

January  1st,  1837. 

•    £     s.      d. 

500       0       C 

■ 

'  1  commenced  business  with  a  capital  of  Five  Hun 
dred  Pounds  in  Cash 

" 

■ 

'IB 

2d. 

73 

60 
133 

12 
6 

7 
0 

fl 

Bennett  and  Sons,  London,*                          Cr 
By  2  hhds.  of  sugar 

cwt.  qr.  lb.         cwt.qr.lb. 
13     1     4             12     0 
12     3  16             116 

1 

gross  wt.  26    C  20 
tare            2    3    6 

1 

neat  wt.  23    1  14  at  633.  per  cwt. 

■ 

2  chests  of  tea 

cwt.  qr.  lb.                    lb. 
1     0  15                     25 
1     0  12                     25 

1 

2    0  27 
1  22 

^^^1 

1     3    5  at  6s.  per  lb 

H 

18 

7 

0 
6 

6 

0 
0 
6 

6 

* 

^1 

3d. 

3 
3 

7 

3 

5 
0 

10 
0 

8 
17 

5 

10 
12 
18 

0 
6 

■  ^ 

■ 

Hall  and  Scott,  Liverpool,                              Cr 
By  soap,  1  cwt.                       at  68s .*. . 

1 

candles,  10  dozen               at  7s.  9d. . . . 

■ 

■ 

6th. 

■ 

TVard,  William                                               j)r,  ~ 
To  1  cwt.  of  sugar,                at  70s 

I 

14  lbs.  of  tea,                     at  8s 

'  '■ 

i  cwt.  of  soap,                   at  74s 

■ 

■ 

6th. 

■ 

Uooper,  William                                              j),.   ~ 
To  1  sugar  hogshead ,\ .' , . 

■ 

m 

k«*i  '''^^  student  may  be  directed  to  fill  up  this  and  similar 'blanks  in  th» 
oook  and  the  Ledger  with  the  names  of  places  familiar  to  him 


y 


202 

DAY  BOOK. 


(foUo  2.) 


2 

1 

2 

1 

2 
2 
2 

Janxiary  9th,  1837. 

£ 

0 

1 
1 

4 

.0 

17 
17 

0 
0 
0 
0 

1 

s. 
16 
17 
15 

8 

5 

0 
5 

9 
8 
4 
8 

10 

d. 

b 
0 
0 

6 

0 

0 
0 

0 
6 
9 
3 

6 
0 

10 
6 

4 

0 
2 

2 

0 
3 

3 

Johnson,  Richard 

To  2  dozen  of  candles               at  8a    3d.. . 

Dr. 

i  cwt   of  soar).                      at  74s«  ••••••••••• 

i  cwt"   of  suff'kr.                    at  70s.  ••••••••••• 

lOth. 

Ward,  William 
To  sugar,  1  cask 

cuit.  qrs,  lb. 
gross  wt.    5    2  ID            cask 
tare                 2  10 

Br. 

neat            5    0    0  at  68s  .... 

12th. 

Smith,  John 
To  14  lb.  of  auerar 

Dr. 

12  lb  of  candles 

7  lb.  of  soao ••••••••• 

1  lb.  of  tea 

14th. 

6 

16 

13 
16 

10 

9 
4 

13 

19 

8 

6 

Hall  and  Scott,  Liverpool, 
Bv  2  cwt.  scan.                           at  6Ss.  •  • 

Cr. 

17th. 

0 
0 

1 

0 
0 

0 

0 
0 

1 

J>tewton,  John 

To  21  lb.  of  soap,                    at  74s.  per  « 
2  dozen  of  candles.          at  Ss.  3d.  •  • 

Dr. 

:wt.... 

i9th. 

Smith,  John 
To  14  lb.  of  sugar 

Dr. 

i  lb.  of  tea 

•  21  St. 

Smith-,  John 
To  28  lb.  of  sugar 

Dr. 

12  lb.  of  candles : ; 

, 

203 


DAY  BOOK 

(folio  3.) 

■ 

2 
3 
2 

2 
2 

3 

3 
3 

1 
3 

January,  23d.,  1837. 

£ 

8 

d. 

0 

0 
6 

6 
0 
0 

H 

Yates  8r  Lane,  Bradford,                                Cr. 
By  'i  pieces  of  superfine  cloth,  each  36  yards, 

at  249.  per  yard... 

« 

17i2 

!    16 

8 

9 

■ 

23d. 

2 

0 

m 

Edwards,  Benj.  Manchester,                         Cr. 
By  2  pieces  of  calico,  each  24  yards,  at  Is.  per  yard 

'^H 

23d. 

^^1 

s 

Smith,  John                                                   Br. 
To  14  lb.  of  soap 

H 

24th. 

0 
3 
5 

9 

16 

14 

5 

a 

Johnson,  Richard                                            Dr. 
To  2  dozen  of  candles.          at  Ss.  3d 

1 

1  cwt.  of  soap,                 at  74s 

■ 

1  k  cwt.  of  sugar,              at  70s 

■ 

l^M 

15 

6 

0 

0 
0 

0 

0 

1 

0 
6 
6 

J 

H 

24th. 

0 

145 

2 
148 

50 

8 

16 

16 
12 

8 

16 

17 
7 

19 
15 

19 

H 

Smith,  Jithn                                                     Dr, 
To  1  lb.  of  tea * . . 

■ 

26th. 

Mason,  Edward                                             J)r. 
To  3  pieces  of  superfine  cloth,  each  36  yards, 

at  27s.  per  yard.... 
2  pieces  of  calico,  each  24  yards, 

at  Is.  2d.  per  yard.. 

27th. 

H 

Parker,  Thomas                                             Br. 
To  1  piece  of  superfine  cloth,  36  yards,  at  28s.. . 

1 

31st. 

172 

■ 

Bills  Payable,                                                    Cr. 
By  Yates  &  Lane's  Bill  at  2  months,  due  April  2. 

1 

Inventory,  January  31,  1837. 

46 

55 

2 

0 

105 

■ 

cwt.  qr.  lb. 
Raw  sugar,                    14    3  14    at  633 

■ 

Tea,                                1     2  16^  at  6s.  per  lb 

Soap,                               0     3  14    at  68s  

M 

Ca . Id ic'S,  2  dozen,                           at  7s.  9d 

'^1 

■ ' 

m 

201 


CASH    BOOK. 


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William  Ward,  Bill 
Richard  Johnson,  C 
John  Smith,  Cash, 
John  Newton,  on  a 
Edward  Mason,  Bil 
Thomas  Parker,  Ca 
My  acceptance  at  2 
from  the  Bill-boo 

1 

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William 
Bernard 

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O  '^  »-•  CO  o  -< 

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205 


INDEX  TO  THE  LEDGER. 

Newton,  Johu. 


Bernard  &  Co. . . .  j" 

B  S?"'**"^  Sons.  London.*.*;  i 
J-'  Bills  payable 3 


0 


C 


Cooper,  William g 


D 


Parker,  Thomas. 


E 


Edwards,  B.  Manchester  ...  3 


Q 


F 


R 


Stock  account 


G 


H 


Hall  &  Scott,  Liverpool. . . .  l 


J 


Johnson,  Richard 2 


K 


W 


Ward,  William 


X 


Q  Smith,  John .*.*;;;;  j 


Yates  &  Lane,  Bradford. ...  2 


M 


Mason,  Edward 3 


206 


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€fi\fih^ut  nf  aJnnltB 


PDBUSHBO  BT 


D.  «&  J.  SADLIEK  &  CO, 


be  in  the  possession  of  every  Cathd  c  fkmflv     Thu  fiu" 
^80  cpntafns  25  fine  steel  enVavings,  and  fou/i  LfnS^^ 

St  DrXaL'' and"!?'  f'ii^^l4proh.Z  of  th"  MobI 
^r*v:  r  rn  ,.^'  ^H^  ^9  Archbishops  and  Bishona  of  tlia 
S?J^fl '° .^^'-^h-prnted  on  the  finest  paper,  sSSer  extra 
tt^:mT  ^'^^^^^^  or  French  stylefsp^hirbSsr^S 

Turkey  super  extra,  $14  00. 

Iinitation  turkqy,  gilt  sides,  spring  backs,  gilt  edges, 

^"^slyt,!!?©??  ^'''^''  "^^  ^'^^'''  '"^  ^^'^"^^  °'  ^g^J«h 
Imitation  calf  extra,  spring  backs,  comb  edges,  $10  00. 
bheep  extra,  spring  backs,  marble  edges,  |8  00. 

inX-^'  P»WUhen  at  the  .olicitation  of  several  clergymen,  being  derirou.  of  extend, 

«.t  the  wanfof  .uch  person,  as  cannot  afford  to  buy  the  more  expen.ire  cople.,  but^ey 
^rongy  recommend  .11  thoee  who  can  pnrcha.e  their  illuBt«tad  edition.  in'an'i^lS 

t^nt      '"  r     *""  **•  ""  "'"'P  ''""•«•  "•  '""»  '»'•  extraordinary  car,  whkh 
thiy  beatow  on  the  prmtmg  and  binding  of  the  former,  they  can  with  the  fUlle.t  confl. 

^IZIT:^^^  ''''-''''  ''-  -  ^'•«^^-'  -''  ^  ^-'^  0^-^'.  «  «^e 

1 


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responding panels,  beautifully  embellished  after  the  anUqiM 
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clasps,  $16  00. 

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THE  HISTORY  OF  THE  VARIATIONS  OF  THE  PROT- 
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of  Meaux.     2  vols.  12mo.  $1  50. 

or  Thi»  U  one  of  th«  mo«t  celebrated  worlu  in  the  Catholic  Library.    It  it  styled  by 
Moeheim,  the  Proteetant  Church  Historian,  "  The  Bulwark  of  Popery," 

WARD'S  ERRATA  OF  THE  PROTESTANT  BIBLE.'  A 
work  showing  the  errors  of  the  Protestant  Translations  of 
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2 


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^'GLWrn'^SrST  ?5  ™F  REPOEMATION  IN  EN- 

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8 


1 


CATALOGUE    OP    BOOKS 


THE  CASTLE  OF  ROUSSILLON ;  ob,  Qu«bot  w  tm  Six- 

TKKNTH  Century.    A  talo,  trunalatod  from  the  French  of 

Madame  Eugknik  uk  Ul  Kociikbk,  by  Mrs.  J.  Saduxb. 

Qoth,  gilt  back-,  60o. 

Steel  phito,  and  illuminated  title,  full  gilt  aides  and  edges, 

75  cuntD. 
Imitation  morocco,  |1  00. 

DUTY  OF  A  CHRISTIAN  TOWARDS  GOD.  Beinff  an  im- 
proved version  of  the  orlj?inal  Trent!  ^o,  written  by  the  Ven- 
erable J.  B.  Sall«,  Founder  of  the  Brothers  of  the  Christian 
School.  Translated  from  the  French  by  Mrs.  J.  Saduki, 
■with  the  l*rayer3  at  Moss  and  the  Rules  of  Christian  Polite- 
ness.   12mo.  400  pages.    The  same,  half  bound,  87*0. 

Muslin,  neat,  50c. 
"       gilt  edges,  75c. 

LIFE  OF  THE  RT.  REV.  DR.  DOYLE,  Bishop  o»  Kiujabb 
AND  Leiohun.    With  a  Portrait. 

Th«  lift  of  thU  Pntriot  Bishop  should  .b«  in  the  houaa  of  every  Ctolbolio ;  more  «fpe- 
eklly  tho«  of  Irish  origiu.  It  give*  •  tummarr  of  bis  examination  W«for8  tho  HouM  of 
Lords,  on  the  Catholic  question.  It  is  a  work  which  every  Iri»h  father  should  place  in 
the  hands  of  Ms  children,  as  Lis  nnme  should  be  engraved  indelibly  upon  the  hoarU  of 
Irlshmeo  and  their  oftbpring. 

BENJAMIN  :  or,  Pupil  or  thk  Christian  Brothers.  Trans- 
lated from  the  Frorich,  by  Mrs.  J.  Sadlier.  24rao.  muslm,  26o. 

Full  gUt,  S7i. 
THE  LIFE  OF  THE  BLESSED  VIRGIN— to  which  is  added 
a  Novena  in  honor  of  Her  Immaculate  Conception,  with  an 
Historical  account  of  the  Origin  and  Effects  of  the  Miraou- 
'  Ions  Medal.    2  plates,  large  type,  82mo,  revised  by  the 
Very  Rev.  Felix  Vakella— full  muslin,  gilt  back,  18|o. 
Full  gilt,  and  gilt  edges,  87ic. 

A  SHORT  HISTORY  OF  THE  FIRST  BEGINNING  AND 
PROGRESS  OF  THE  PROTESTANT  RELIGION,  by  way 
of  Question  and  Answer.    By  Bishop  Cualloneb.   A  moet 

:  excellent  and  instructive  work.  ISmo.,  clear  type.  Full 
muslin,  18c; 

DOUAY  TFi^TAMENT,  with  am*,  -ii ions,  and  chronoiogical 

-■•'  '•'■'^nm  'Mr^i-   ''  .  MV       John 


and  analytical  tables,  as  approve^?  o^  I  y ' ''O  Most ' 


..PV 


iSr'iO.  full  muslin,  em- 


Hughes,  Archbishop  of  New 
bossed,  gilt  back,  87io. 

ART  MAGUIRE;  or,  The  Broken  Pledoe.    By  Wiluam 

r    Carleton.  Author  of  "  Traits  and  Stories  of  the  Irish  Peas- 
antry.'"   Dedicated  to  the  Very  Rev.  Theobald  Mathew. 


m 


_PT7BLISHED   BY    D.    ^    j.    s.dlIER 


4    CO. 


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EVEMNO   8KRVICR   Or  THE  CW.f.    p"'    ^""^    ^««^NO   AND 

choice  collection  of  G^-c-'orhm  aS  ^^'""xV   ^'"»«r'»i"K  » 
l*8nlin8,  Sacred   Ifvinn«    Anl\  *',^''^**  Mumsos,  LitmifeB 

selected  «n,l  new/a "ra^t" t V/'"^'^'^^'  '^"'^  ^o  i?',' 
first  masters.    Comnilfi.rf,!.  i       "  ^''?  ^compositions  of  the 

THE  CATHOLIC  HARP  o     .  •  ^^^  ^^"'  ^^-    «^  00. 
ing  Service  oYt["a,?i^^o'li?fr'^^  the  Morning  «nd  Even- 

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CATHOLIC  PRAYER  BOOKS. 

for  b«.„ty  of°flS,rr"bilS''oA'I,M"  '"'"''"'  ""  ""•  P-P*'. «-  <"*»'.  bold  type  «d 

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t..n  uvea  .„  .he  pW„U„,  and  hMif;:,  :^;.f  S;:,  /o^ir  *  ^'"-'"  "'""  »-- 

THE  GOLDEN  M A NTTAT  .  1    • 

tion,  Public  and  Privafe'CornL'd^"'^''  ^°  ^'^^h°"«  ^evo- 
18mo.,  1041  pages.  ^ofnp'lcd  from  approved  sources. 

Neatly  bound  iu  aheep,  1  nlate  H   T-i 
Joan,  plftin  P'     C^e,  f   75. 

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"    ,^iit,        ^.^  «         Jj- 


An.riatnWo,gm 

Morocco,  extra  illiimin„f^j        «      '         2  00. 


2  50. 
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clasps,  jj  5^5 

^  th;^^'«Ii.h  lanKuago.  The  ^a/er^^'ilrr^T' r"^""' *^"P"'''»''«'' 
Ihe  UUn  oriKi,uiU,  wherever  .uch  were  k  .ow?;  ■  .  '  ^^^  ^'^  '=°"*t«d  with 
P-lin.  here  pven  ha.  bee«  co„,truc7ed  bv^rol  """'  '^'"'  ^"«""'  ^^"'o"  of  the 
(to  which,  in  .uutance.  it  adhereS  wUh  h!  Lve'^Ut;; "'  '"".'"""--I  »o"ay  text 
t.n..  have  been  .onctionea  for  the  pT  11  tf  dZ  °""'.'Lr™0''*  ^^ch  f^om  time  to 
been  literally  tra„„ated  from  the  R^tr^uver. '  r'  I'"'  """'^•"""'  P^^-  '"'ve 
»«t  edition  of  .he  Cosleate  Palmet,.r  Se^X.  ""'  °"  "«'"'&<"><='"•.  and  th, 
t> e.,  Ac,  to  which  indulgence,  are  at^^.hed  haCt  '?""''*'*  *'"»  ">«  Confratemi- 

-.rce..  and  published  with  the  appri.  o^oTb^E^    ""^"""''''*  ^™™  ""thori^d 
prewnt  edition  ha.  been  enlarirerf  wUh  Eminence,  Cardinal  Wi,eraan     Th« 

-nn,  and  .election.  ftT^:^^^:^^^^^  '""•^"'"-  '^'"  *"*  ^'-""^i  lit 
office,  of  the  IHeued  Virgin  Lrthrlolr°:."''^'  together  with  the  complet. 

pi-ation.  of  all  the  f»ii.L7i';z'^i,T.::^2  TtT  ''•' '""''  -^ « 

•fylea  of  binding :_  '  ""•  ^'"''^  «*"»  oK  b«  had  in  the  followinr 


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THE  GARDEN  OF  THE  SOUL.  A  Manual  of  fervent 
Prav-erl  pious  Eeflections,  and  solid  Instructions,  calculated 
fo^nswe?  ?he  use  of  the  members  of  all  ranks  and  con^- 
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HISTORY  OF  lEELAND,— ancient  and  modem,  taken  from 
the  most  authentic  records,  and  dedicated  to  the  Irish 
Brigade,  by  the  Abb6  MacGeoghegan.  Translated  from 
the  French,  by  Patrick  O'Kelley,  Esq.,  with  4  fine  steel 
engravings. 

"  Ha  is  graphic,  easy,  and  Irish.  Ho  ii  not  a  bigot,  but  appareatly  a  gennine  CathoUe. 
His  ioformation  as  to  th«  number  of  troops  and  other  facts  of  our  Irish  battles,  is  superior 
to  any  other  general  historian,  and  they  who  know  it  well  need  not  blush,  as  most  Iriah- 
men  must  now,  at  their  ignorance  of  Irish  history."— TAomo*  2>a«w,  En»if  en  IHihHU- 
tory, 

THE  EISE  AND  FALL  OF  THE  IRISH  NATION,  by  Sir 
Josiah  Barriugtou ;  late  Member  of  tlie  Irish  Parliament  for 
the  Cities  of  Tuam  and  Clogher.  It  contains  twenty-nine 
portraits  of  celebrated  men  who  figured  in  the  Irish  Parlia- 
ment. 

The  above  work  iit  admitted  by  competent  Jidges  to  be  om  of  the  nost  beaatifal  pro. 
ductions  of  the  day.  It  was  sold  in  Dublin,  when  first  published,  at  $10.  Soch  is  iti 
intrinsic  merits,  that  it  iias  been  admitted  by  the  Snperintendent  of  PubUo  Schools  iato 
the  District  School  libraries  of  the  various  States.  No  Irishman,  who  !•  desirooa  of  be- 
commg  acquainted  with  that  epoch  of  his  countrj-'s  history — the  rise  of  the  volunteers— 
the  declaration  of  rights— and  the  debates  conneeted  with  that  tynumoua  act,  the  Legis- 
lative Union,  should  iail  to  possess  himself  of  a  copy  of  this  admirable  work. 

VALENTINE  MoCLUTCHY,  THE  IRISH  AGENT;  by 
Carleton.  8  vols,  of  the  Dublin  edition,  in  one.  Muslin,  76 
cents ;  half  bound  50  cents. 

In  this  work  Mr.  Carleton  has  depicted  the  wrongs  and  suflbrings  of  his  eoontrymen— 
their  patience  and  forbearance  under  their  sufferings ;  and  in  the  character  of  Valentine 
McClutchy  he  shows  the  villany  practised,  by  the  agents  of  absentee  landlords,  apon 
those  tenants  who  are  ao  nofbrtimate  as  to  hold  lands  tram  them ;  and  a*  a  speeimea  of 
a  religious  attorney,  we  would  challenge  creation  to  produce  a  more  correct  picture  than 
that  drawn  by  Carietiiini  «f  Solomon  McShine.  We  venture  to  say  that  there  It  net  •■ 
Irishman,  who  waal^iM  ten  pagee  of  the  work,  that  would  be  without  it  for  ten  tiniM 
the  cost. 


■uMi-. 


